Entropic repulsion for the occupation-time field of random interlacements conditioned on disconnection

We investigate percolation of the vacant set of random interlacements on $\mathbb{Z}^d$, $d\geq 3$, in the strongly percolative regime. We consider the event that the interlacement set at level $u$ disconnects the discrete blow-up of a compact set $A\subseteq \mathbb{R}^d$ from the boundary of an enclosing box. We derive asymptotic large deviation upper bounds on the probability that the local averages of the occupation times deviate from a specific function depending on the harmonic potential of $A$, when disconnection occurs. If certain critical levels coincide, which is plausible but open at the moment, these bounds imply that conditionally on disconnection, the occupation-time profile undergoes an entropic push governed by a specific function depending on $A$. Similar entropic repulsion phenomena conditioned on disconnection by level-sets of the discrete Gaussian free field on $\mathbb{Z}^d$, $d \geq 3$, have been obtained by the authors in arxiv:1808.09947. Our proofs rely crucially on the `solidification estimates' developed in arXiv:1706.07229 by A.-S. Sznitman and the second author.Comment: 35 pages, 2 figures, accepted in the Annals of Probabilit

Disconnection by level sets of the discrete Gaussian free field and entropic repulsion

We derive asymptotic upper and lower bounds on the large deviation probability that the level set of the Gaussian free field on $Z^d$, d bigger or equal to three, below a given level disconnects the discrete blow-up of a compact set A from the boundary of the discrete blow-up of a box that contains A, when the level set of the Gaussian free field above this level is in a strongly percolative regime. These bounds substantially strengthen the results of arXiv:1412.3960, where A was a box and the convexity of A played an important role in the proof. We also derive an asymptotic upper bound on the probability that the average of the Gaussian free field well inside the discrete blow-up of A is above a certain level when disconnection occurs. The derivation of the upper bounds uses the solidification estimates for porous interfaces that were derived in the work arXiv:1706.07229 of A.-S. Sznitman and the author to treat a similar disconnection problem for the vacant set of random interlacements. If certain critical levels for the Gaussian free field coincide, an open question at the moment, the asymptotic upper and lower bounds that we obtain for the disconnection probability match in principal order, and conditioning on disconnection lowers the average of the Gaussian free field well inside the discrete blow-up of A, which can be understood as entropic repulsion.Comment: 23 pages, 1 figure, appeared in the Electronic Journal of Probabilit

Disconnection and entropic repulsion for the harmonic crystal with random conductances

We study level-set percolation for the harmonic crystal on $\mathbb{Z}^d$, $d \geq 3$, with uniformly elliptic random conductances. We prove that this model undergoes a non-trivial phase transition at a critical level that is almost surely constant under the environment measure. Moreover, we study the disconnection event that the level-set of this field below a level $\alpha$ disconnects the discrete blow-up of a compact set $A \subseteq \mathbb{R}^d$ from the boundary of an enclosing box. We obtain quenched asymptotic upper and lower bounds on its probability in terms of the homogenized capacity of $A$, utilizing results from Neukamm, Sch\"affner and Schl\"omerkemper, see arXiv:1606.06533. Furthermore, we give upper bounds on the probability that a local average of the field deviates from some profile function depending on $A$, when disconnection occurs. The upper and lower bounds concerning disconnection that we derive are plausibly matching at leading order. In this case, this work shows that conditioning on disconnection leads to an entropic push-down of the field. The results in this article generalize the findings of arXiv:1802.02518 and arXiv:1808.09947 by the authors which treat the case of constant conductances. Our proofs involve novel "solidification estimates" for random walks, which are similar in nature to the corresponding estimates for Brownian motion derived by Sznitman and the second author in arXiv:1706.07229.Comment: 58 pages, 2 figures, to appear in Communications in Mathematical Physic

Lower bounds for bulk deviations for the simple random walk on Zd\mathbb{Z}^d, d≥3d\geq 3

This article investigates the behavior of the continuous-time simple random walk on $\mathbb{Z}^d$, $d \geq 3$. We derive an asymptotic lower bound on the principal exponential rate of decay for the probability that the average value over a large box of some non-decreasing local function of the field of occupation times of the walk exceeds a given positive value. This bound matches at leading order the corresponding upper bound derived by Sznitman in arXiv:1906.05809, and is given in terms of a certain constrained minimum of the Dirichlet energy of functions on $\mathbb{R}^d$ decaying at infinity. Our proof utilizes a version of tilted random walks, a model originally constructed by Li in arXiv:1412.3959 to derive lower bounds on the probability of the event that the trace of a simple random walk disconnects a macroscopic set from an enclosing box.Comment: 49 pages, 1 figur

Quantitative equilibrium fluctuations for interacting particle systems

We consider a class of interacting particle systems in continuous space of non-gradient type, which are reversible with respect to Poisson point processes with constant density. For these models, a rate of convergence was recently obtained in 10.1214/22-AOP1573 for certain finite-volume approximations of the bulk diffusion matrix. Here, we show how to leverage this to obtain quantitative versions of a number of results capturing the large-scale fluctuations of these systems, such as the convergence of two-point correlation functions and the Green-Kubo formula.Comment: 28 page

RFID-Einführung in den Städtischen Bibliotheken Dresden: Größte Stadtteilbibliothek startet nach Umzug mit neuer Technik

Es ist morgens kurz nach sechs Uhr. Eine Nutzerin hält eine DVD an die Fensterscheibe der Bibliothek. Die Tür zum Windfang öffnet sich. Einige Meter weiter befindet sich ein in der Wand eingebauter Rückgabeautomat, in den die DVD kurze Zeit später eingezogen und in einen der drei Sammelbehälter verteilt wird. Die Stadtteilbibliothek Dresden Neustadt hat die 24-Stunden-Rückgabe auf Grundlage der RFID-Technik (engl. radio-frequency identification) realisiert. Wie bei der Einführung der EDV-Verbuchung 20 Jahre vorher ist sie die Pilotbibliothek im Dresdner Stadtnetz

Konzeption und Entwicklung eines Online-Tutorials zur Verbesserung der Informationskompetenz von Studierenden der Elektrotechnik/ Informationstechnik

Verschiedene Studien belegen, dass vor allem Studierende oft keine ausreichenden Kenntnisse, Fähigkeiten und Fertigkeiten besitzen, um das zunehmende Angebot elektronischer Informationsressourcen zu überschauen und effektiv zu nutzen. Besonders im Bereich der wissenschaftlichen Bibliotheken werden deshalb zahlreiche Schulungsveranstaltungen zur Verbesserung der Informationskompetenz durchgeführt. Um den veränderten Bedürfnissen der Nutzer nach einer größeren Flexibilität hinsichtlich ihrer Lern- und Arbeitsorganisation gerecht zu werden, bedarf es der Schaffung zusätzlicher, zeit- und ortsunabhängiger Schulungsangebote. In der vorliegenden Arbeit werden die entscheidenden Faktoren für einen erfolgreichen Einsatz von E-Learning-Anwendungen benannt und unter Berücksichtigung dieser Kriterien ein Online-Tutorial zur Recherche in den Fachdatenbanken der Elektrotechnik, Elektronik und Nachrichtentechnik an der SLUB Dresden konzipiert. Der Planungsphase schloss sich die technische Umsetzung an

Side matters:potential mechanisms underlying dogs' performance in a social eavesdropping paradigm

Social eavesdropping is the gathering of information by observing interactions between other individuals. Previous studies have claimed that dogs, Canis familiaris, are able to use information obtained via social eavesdropping, that is, preferring a generous over a selfish human donor. However, in these studies the side was constant between the demonstrations and the dogs' choices, not controlling for potential location biases. In the crucial control condition of our experiments, the donors swapped places in half of the trials before the dogs chose. We found that first choice behaviour as well as the time dogs interacted with the generous donor were influenced by location (side). In a second experiment the subject's owner interacted with the two donors. Again, the result of the side control revealed that the critical factor was location (side) not person. The results of these experiments provide no evidence for social eavesdropping in dogs and show the importance of critical control conditions