Free energy fluctuations for directed polymers in random media in 1+1 dimension

We consider two models for directed polymers in space-time independent random media (the O'Connell-Yor semi-discrete directed polymer and the continuum directed random polymer) at positive temperature and prove their KPZ universality via asymptotic analysis of exact Fredholm determinant formulas for the Laplace transform of their partition functions. In particular, we show that for large time tau, the probability distributions for the free energy fluctuations, when rescaled by tau^{1/3}, converges to the GUE Tracy-Widom distribution. We also consider the effect of boundary perturbations to the quenched random media on the limiting free energy statistics. For the semi-discrete directed polymer, when the drifts of a finite number of the Brownian motions forming the quenched random media are critically tuned, the statistics are instead governed by the limiting Baik-Ben Arous-Peche distributions from spiked random matrix theory. For the continuum polymer, the boundary perturbations correspond to choosing the initial data for the stochastic heat equation from a particular class, and likewise for its logarithm -- the Kardar-Parisi-Zhang equation. The Laplace transform formula we prove can be inverted to give the one-point probability distribution of the solution to these stochastic PDEs for the class of initial data.Comment: 73 pages, 10 figure

Universality of slow decorrelation in KPZ growth

There has been much success in describing the limiting spatial fluctuations of growth models in the Kardar-Parisi-Zhang (KPZ) universality class. A proper rescaling of time should introduce a non-trivial temporal dimension to these limiting fluctuations. In one-dimension, the KPZ class has the dynamical scaling exponent $z=3/2$, that means one should find a universal space-time limiting process under the scaling of time as $t\,T$, space like $t^{2/3} X$ and fluctuations like $t^{1/3}$ as $t\to\infty$. In this paper we provide evidence for this belief. We prove that under certain hypotheses, growth models display temporal slow decorrelation. That is to say that in the scalings above, the limiting spatial process for times $t\, T$ and $t\, T+t^{\nu}$ are identical, for any $\nu<1$. The hypotheses are known to be satisfied for certain last passage percolation models, the polynuclear growth model, and the totally / partially asymmetric simple exclusion process. Using slow decorrelation we may extend known fluctuation limit results to space-time regions where correlation functions are unknown. The approach we develop requires the minimal expected hypotheses for slow decorrelation to hold and provides a simple and intuitive proof which applied to a wide variety of models.Comment: Exposition improved, typos correcte

Limit processes for TASEP with shocks and rarefaction fans

We consider the totally asymmetric simple exclusion process (TASEP) with two-sided Bernoulli initial condition, i.e., with left density rho_- and right density rho_+. We consider the associated height function, whose discrete gradient is given by the particle occurrences. Macroscopically one has a deterministic limit shape with a shock or a rarefaction fan depending on the values of rho_{+/-}. We characterize the large time scaling limit of the fluctuations as a function of the densities rho_{+/-} and of the different macroscopic regions. Moreover, using a slow decorrelation phenomena, the results are extended from fixed time to the whole space-time, except along the some directions (the characteristic solutions of the related Burgers equation) where the problem is still open. On the way to proving the results for TASEP, we obtain the limit processes for the fluctuations in a class of corner growth processes with external sources, of equivalently for the last passage time in a directed percolation model with two-sided boundary conditions. Additionally, we provide analogous results for eigenvalues of perturbed complex Wishart (sample covariance) matrices.Comment: 46 pages, 3 figures, LaTeX; Extended explanations in the first two section

Height fluctuations for the stationary KPZ equation

We compute the one-point probability distribution for the stationary KPZ equation (i.e. initial data H(0,X)=B(X), for B(X) a two-sided standard Brownian motion) and show that as time T goes to infinity, the fluctuations of the height function H(T,X) grow like T^{1/3} and converge to those previously encountered in the study of the stationary totally asymmetric simple exclusion process, polynuclear growth model and last passage percolation. The starting point for this work is our derivation of a Fredholm determinant formula for Macdonald processes which degenerates to a corresponding formula for Whittaker processes. We relate this to a polymer model which mixes the semi-discrete and log-gamma random polymers. A special case of this model has a limit to the KPZ equation with initial data given by a two-sided Brownian motion with drift beta to the left of the origin and b to the right of the origin. The Fredholm determinant has a limit for beta>b, and the case where beta=b (corresponding to the stationary initial data) follows from an analytic continuation argument.Comment: 91 pages, 8 figure

Chapter San Cataldo (Lecce, Italy): The Historical Evolution Of The Coastal Landscape

San Cataldo is located on the Adriatic sea about 10 km east from Lecce (Italy). Since ancient times it was a port and the remains of a Roman pier are visible: the study illustrate the evolution of its coastal landscape from historical origins until today. The port was renovated in medieval times and also between the 19th and 20th centuries with the construction of a lighthouse, a new pier and a tramway with Lecce. During the last century emerged the tourist vocation of San Cataldo with events of overbuilding characterizing the nowadays coastal landscape

El muelle romano de San Cataldo: de los datos arqueológicos a la reconstrucción 3D

[EN] The pier of San Cataldo (Lecce, Italy) is located along the Adriatic coast about 10 km east-northeast of the ancient city of Lupiae, (today's Lecce), and is the best-preserved port structure of the Roman Age in Apulia. It was researched between 2004 and 2007 by the Laboratory of Topography and Photogrammetry (LabTAF) of the University of Salento, who produced a detailed analysis of the remain and a survey of the portion still visible on the mainland. At the same time, aerial surveys and the study of historic aerial photos from the 1940s and 50s supported a topographic study of the site. Since 2013, within the activities of the LabTAF, the structure has been the subject of an excavation campaign where a further portion of the pier was discovered in the mainland, and the underwater remains were documented. This contribution aims to emphasise the importance of collecting complete metric and historical-archaeological data for a proper three-dimensional (3D) reconstruction of the structure. On this occasion a photogrammetric survey was conducted and a 3D image-based model created that has become the starting point of the reconstruction hypothesis of the pier and its topographical context. The final model represents a reasonable synthesis of the interpretation of the collected data, and serves as a starting point for tackling the future integration or modification of the structure.Highlights:A key requirement for a better understanding of the Roman pier of San Cataldo (Lecce, Italy) was the creation of a 3D model from an image-based survey.The 3D reconstruction process of the monument was based on a production pipeline anchored to metric data and historical-archaeological information.The final 3D reconstruction proposal shows the original shape of the Roman pier, the ancient surrounding landscape and its related activities.[ES] El muelle de San Cataldo (Lecce, Italia) está situado en la costa adriática a unos 10 km en dirección este-noreste desde la antigüa ciudad de Lupiae (actual Lecce), y es una de las estructuras portuarias de edad romana mejor conservadas de Apulia. La investigación se llevó a cabo entre 2004 y 2007 por parte del Laboratorio de Topografía y Fotogrametría (LabTAF) de la Universidad del Salento, que produjo un análisis detallados de los restos y la topografía de la porción visible en la tierra firme. Al mismo tiempo, se realizon vuelos aéreos y se estudiaron las fotografías aéreas históricas de los años 1940 y 50, dando lugar a un estudio topográfico del sitio. Desde 2013, como parte de las actividades del LabTAF, la estructura ha sido objeto de una campaña de excavación arqueologica que desenterró una ulterior porción del muelle en tierra firme, y se documentaron los restos sumergidos. Esta contribución quiere enfatizar la importancia de abordar la reconstrucción tridimensional (3D) fiel de la estructura, siendo necesarios todos los datos métricos e histórico-arqueológicos. En esta ocasión, se realizó un levantamiento fotogramétrico y un modelo 3D basado en imágenes como punto de partida para realizar la hipótesis de reconstrucción del muelle y de su contexto topográfico. El modelo final representa una síntesis razonable de la interpretación de los datos recogidos, y sirve como punto de partida para abordar la futura integración o modificación de la estructura.The authors are grateful to Prof. Giuseppe Ceraudo and Prof. Carla Maria Amici (University of Salento, coordinators of the Portus Lupiae project) and to Drs.Silvia Marchi and Mariangela Sammarco for their technical-scientific support given to carry out the documentation and study of the Roman pier of San Cataldo.Ferrari, I.; Quarta, A. (2019). The Roman pier of San Cataldo: from archaeological data to 3D reconstruction. Virtual Archaeology Review. 10(20):28-39. https://doi.org/10.4995/var.2019.795728391020Auriemma, R. (2004). Salentum a Salo: Porti, approdi, merci e scambi lungo la costa adriatica del Salento. Galatina: Congedo Editore.Barbon, F. H. (2005). I segni dei mercanti al Fondaco dei Tedeschi. In Actes du XIV Colloque International de Glyptographie de Chambord (19-23 juillet 2004) (pp. 5-55). Belgium: C.I.R.G.Brandon, C., Hohlfelder, R. L., Oleson, J. P., & Rauh, N. (2010). Geology, Materials, and the Design of the Roman Harbour of Soli-Pompeiopolis, Turkey: the ROMACONS field campaign of August 2009. The International Journal of Nautical Archaeology, 39(2), 390-399. doi:10.1111/j.1095-9270.2010.00277.xBrandon, C. J., Hohlfelder, R. L., Jackson, M. D., & Oleson, J. P. (2014). Building for eternity. The history and technology of Roman concrete engineering in the sea, Oxford: Oxbow Books.Caruso, F., Gabellone, F., Ferrari, I., & Giuri, F. (2015). Nuove proposte ricostruttive per una rilettura critica della documentazione archeologica su Siracusa in età greca. Virtual Archaeology Review, 6(11), 115-121. doi:10.4995/var.2015.4149Cecchi Aste, E. (2010). Di mio nome e segno. "Marche" di mercanti nel carteggio Datini (secc. XIV-XV). Prato: Istituto di Studi Storici Postali.Ceraudo, G. (2008). Aerial archaeology in Italy. Recent research and future prospects. The contribution of the LabTAF at the University of Salento. Archeologia Area, 3, 219-232.Ceraudo, G., & Esposito, F. (1997). Strutture sommerse a San Cataldo (Le). In Atti del Convegno nazionale di Archeologia Subacquea (Anzio 30/5 - 1/6 1996) (pp. 241-244). Bari, Italy.Chiabrando, F., D'Andria, F., Sammartano, G., & Spanò, A. (2018). UAV photogrammetry for archaeological site survey. 3D models at the Hierapolis in Phrygia (Turkey). Virtual Archaeology Review, 9(18), 28-43. doi:10.4995/var.2018.5958De Ferraris, A. (1558). Liber de Situ Iapygiae. Basilea: Petrum Pernam (reprint 2005. Galatina: Congedo Editore).De Giorgi, C. (1888). La Provincia di Lecce. Bozzetti di viaggio, II. Lecce: Spacciante (reprint 1975. Galatina: Congedo Editore).De Giorgi, C. (1913). La voce del mare: poche parole dette agli alunni della II classe dell'Istituto Tecnico di Lecce sulla spiaggia di S. Cataldo sull'Adriatico il 17 maggio 1913. Lecce, Italy.De Simone, L. G. (1874). Lecce e i suoi monumenti, I. Lecce: Campanella (reprint 1964. Lecce: Centro Studi Salentini).Ferrari, I., & Giuri, F. (2015). Rilievo e restituzione grafica delle aree delle pozzelle di Pirro e di Apigliano. In A. Chiga, P. Durante, & S. Giammaruco (Eds), Conservare l'acqua. Le Pozzelle di Zollino tra memoria storica e indagini scientifiche (pp. 63-70). Galatina: Editrice Salentina.Ferrari, I., Quarta, A., Sammarco, M., Carpentieri, A., & Di Tondo, A. (2016). Portus Lupiae. 3D modeling and digital storytelling for reconstruction a long maritime history. In Proceedings of the 8th International Congress on Archaeology, Computer Graphics, Cultural Heritage and Innovation 'ARQUEOLOGICA 2.0' (pp. 452-455). Valencia, Spain.Gabellone, F., Ferrari, I., Giuri, F., & Limoncelli, M. (2011). Virtual Hierapolis: tra tecnicismo e realismo. Virtual Archaeology Review, 2(3), 131-136. doi:10.4995/var.2011.4646Gabellone, F. (2013). Il Santuario di Jupiter Anxur a Terracina, studio ricostruttivo tipologico come ausilio per la visita in situ. Virtual Archaeology Review, 4(9), 108-115. doi:10.4995/var.2013.4260Gabellone, F., Giannotta, M. T., Ferrari, I., & Dell'Aglio, A. (2014a). Marta Racconta, A project for the virtual enjoyment of inaccessible monuments. In Proceedings of the 18th International Conference on Cultural Heritage and New Technologies 2013 (CHNT 18, 2013) (pp. 1-14). Vienna, Austria. http://www.chnt.at/wp-content/uploads/Gabellone_etal_2_2014.pdfGabellone, F., Tanasi, D., & Ferrari, I. (2014b). Virtual Archaeology and Historical Revisionism, The Neglected Heritage of Greek Siracusa. In Proceedings of the 18th International Conference on Cultural Heritage and New Technologies 2013 (CHNT 18, 2013) (pp. 130-142). Vienna, Austria. http://www.chnt.at/wp-content/uploads/Gabellone_etal_2014.pdfGabellone, F., Ferrari, I., & Giuri, F. (2015a). Digital restoration using Image-Based 3D models. In Proceedings of the 1st International Conference on Metrology for Archaeology (pp. 478-482). Benevento, Italy.Gabellone, F., Ferrari, I., Giuri, F., & Chiffi, M. (2015b). The contribution of the 3D study for new reconstructive proposals of Lecce in Roman age. In Proceedings of the 1st International Conference on Metrology for Archaeology (pp. 534-538). Benevento, Italy.Gabellone, F., Ferrari, I., & Giuri, F. (2017a). A new contribution for the reconstructive study of the theatre of Taormina. In Proceedings of IMEKO International Conference on Metrology for Archaeology and Cultural Heritage (pp. 601-606). Lecce, Italy.Gabellone, F., Ferrari, I., Giuri, F., & Chiffi M. (2017b). Image-Based techniques for the virtualization of Egyptian contexts. In Proceedings of IMEKO International Conference on Metrology for Archaeology and Cultural Heritage (pp. 595-600). Lecce, Italy.Laudisa, I. (1995). Ritratto di una città. Storia della fotografia leccese dell'Ottocento. Lecce: Edizioni del Grifo.Marciano, G. (1855). Descrizione, Origini e Successi della Provincia d'Otranto. Napoli: Stamperia dell'Iride.Merico, A., & Sammarco, M. (2014). Archaeological Landscapes of Southern Apulia: Integration and Interpretation of Gis-Based Data in a Multi-Methodological Research. In LAC2014 Proceedings (pp. 1-8). doi:10.5463/lac.2014.45Sammarco, M., & Marchi, S. (2008). Il porto antico di San Cataldo (Lecce): indagini tradizionali e nuove metodologie per uno studio topografico. Archeologia Aerea. Studi di Aerotopografia archeologica, 3, 147-176.Sammarco, M., & Marchi, S. (2012). Tra terra e mare: ricerche lungo la costa di San Cataldo (Lecce). Journal of Ancient Topography, XXII, 107-132.Sammarco, M., & Marchi, S. (2014). Archeologia costiera a San Cataldo (Lecce). In Atti del III Convegno di Archeologia Subacquea (pp. 27-32). Bari: Edipuglia.Valchera, A., & Zampolini Faustini, S. (1997). Documenti per una carta archeologica della Puglia meridionale. In M. Guaitoli, (Ed.), Metodologie di catalogazione dei beni archeologici. Beni Archeologici Conoscenze e Tecnologie CNR-Università di Lecce, Quaderno 1.2 (pp. 103-158). Bari: Edipuglia

A Quick Method for the Texture Mapping of Meshes Acquired by Laser Scanner

The methodology described in this article was developed in connection with two different projects and entails texture mapping by time-of-flight laser scanner. In order to verify its operational effectiveness and applicability to other contexts, sites with extremely different morphological characteristics were studied. The basic rationale of this simple method derives from the need to obtain different types of mapping – including RGB real colour images, infra-red images, false colour images from georadar scans, etc. – from the same scanned surface. To resolve this problem, we felt that the most appropriate step was to obtain a UVW mapping based on the high resolution real colour images and then use the samecoordinates to rapidly map the false colour images as well. Thus we fitted a device to the camera to determine its trajectory (similar to a gunsight); when scanned by the laser scanner in the same context as the monument, it makes it possible to know the exact coordinates of the viewpoint

La statuetta indiana da Pompei: nuove considerazioni per un approccio emico

Sin dalla sua scoperta a Pompei nel 1938, la statuetta in avorio di manifattura indiana non ha smesso di porre interrogativi sul suo soggetto, sulla sua provenienza, sulla sua funzione prima di arrivare nel municipium campano. In questo contributo, dopo una disamina dello status quaestionis sulla statuetta (datazione, possibile iconografia, provenienza, contesto di rinvenimento) ci si chiederà chi potesse essere il suo proprietario e che cosa avrebbe potuto rappresentare per lui un manufatto tanto particolare. Una risposta potrebbe giungere dalle Metamorfosi di Ovidio, in particolare da una sezione del decimo libro dedicata a miti connessi con l’avorio e la prostituzione femminile, e dall’usanza romana di esporre, durante i banchetti, oggetti curiosi per stimolare la conversazione. Since its discovery, which took place in Pompeii in 1938, the ivory statuette of Indian manufacture has not stopped asking questions about its subject, its origin, its function before its arrival in the Roman municipium. In this paper, after an examination of the status quaestionis on the statuette (dating, possible iconography, provenance, context of discovery) I will try to understand who could be its owner and therefore what a Pompeian of the first century could have seen in such a particular artifact. An answer may come from Ovid's Metamorphoses, in particular from a section of the tenth book dedicated to myths associated with ivory and female prostitution, and from the Roman custom to exhibit curious objects to stimulate conversation during banquets

Height Fluctuations for the Stationary KPZ Equation

We compute the one-point probability distribution for the stationary KPZ equation (i.e. initial data H(0,X)=B(X), for B(X) a two-sided standard Brownian motion) and show that as time T goes to infinity, the fluctuations of the height function H(T,X) grow like T[superscript 1/3] and converge to those previously encountered in the study of the stationary totally asymmetric simple exclusion process, polynuclear growth model and last passage percolation. The starting point for this work is our derivation of a Fredholm determinant formula for Macdonald processes which degenerates to a corresponding formula for Whittaker processes. We relate this to a polymer model which mixes the semi-discrete and log-gamma random polymers. A special case of this model has a limit to the KPZ equation with initial data given by a two-sided Brownian motion with drift ß to the left of the origin and b to the right of the origin. The Fredholm determinant has a limit for ß > b, and the case where ß = b (corresponding to the stationary initial data) follows from an analytic continuation argument.National Science Foundation (U.S.) (grant DMS-1208998)Microsoft ResearchMassachusetts Institute of Technology (Schramm Memorial Fellowship)Clay Mathematics Institute (Clay Research Fellowship)Institut Henri Poincare (Poincare Chair

VIDEOS AUTOEXPLICATIVOS PARA EL MUSEO EGIPCIO DE TURÍN

[EN] In the present project for the setting of the new Museo Egizio of Turin the “cultural message” has been charged to make a few specific 3D computer graphic (CG) movies, and aims to introduce the topics dealt with the rooms dedicated to queen Nefertari, the chapel of the painter Maia and the tomb of Kha, respectively. In these movies, the passivity of viewing is counteracted with an emotional approach that involves the visitor within an informative path where, despite of the inactive kind of interaction, the viewer is somehow involved in the events because he or she is emotionally invested in them. Thanks to this passive and “self-explaining” approach, the visitor will be enabled to understand the relations between different objects, some of which are not directly visible. Moreover, the visitor will be able to virtually insert the tombs within their original context and above all will have the possibility to visit them as they appeared at the moment of their discovery. This has been made possible thanks the use of integrated technologies of representation, able to enhance the virtualization process to a verisimilar level allowing a hyper-realistic and “participative” vision. The high level of realism of the virtual reconstruction, the visual effects and the cinematographic representation, with added emotions to the scientific contents, positively contribute to the “dreamlike displacement” of the visitor between the real and the virtual dimensions.[ES] En este proyecto para la construcción del nuevo Museo Egipcio de Turín el mensaje cultural fue dado a tres películas específicas en gráficos 3D, destinados a la introducción de los temas tratados en las salas dedicadas a la reina Nefertari, la capilla del pintor Maia y la tumba de Kha. En estas películas, la pasividad de la visión se ve compensado por un enfoque emocional que implica el visitante en un trayecto de información en el que, a pesar de la falta de actividad de disfrute, él es en realidad participante, porque emocionalmente involucrado. Gracias a este método, pasivo y “autoexplicativa” el visitante puede comprender las relaciones entre diferentes objetos, algunos no directamente visibles, como la momia de Kha y su esposa Merit, a ser posible reconstruir las tumbas en su contexto original, pero sobre todo la posibilidad de visitar, gracias a las técnicas de la arqueología virtuales, tales contextos como aparecieron en el momento de su descubrimiento. Todo esto es posible gracias a la utilización de tecnologías integradas para el estudio y la representación, capaz de llevar el proceso de virtualización a un grado de verosimilitud hiperrealista y “participativa”. El alto grado de realismo de las reconstrucciones virtuales, efectos visuales y técnicas de representación cinematográfica, añadiendo emoción al contenido científico, contribuyen positivamente a la “pérdida” del visitante entre el real y el tamaño dimensión virtual.Gabellone, F.; Ferrari, I.; Giuri, F.; Chiffi, M. (2016). SELF-EXPLAINING VIDEOS FOR THE MUSEO EGIZIO IN TURIN. En 8th International congress on archaeology, computer graphics, cultural heritage and innovation. Editorial Universitat Politècnica de València. 132-137. https://doi.org/10.4995/arqueologica8.2016.3550OCS13213