Interlacing Patterns in Exclusion Processes and Random Matrices

In the last decade, there has been increasing interest in the fields of random matrices, interacting particle systems, stochastic growth models, and the connections between these areas. For instance, several objects that appear in the limit of large matrices also arise in the long-time limit for interacting particles and growth models. Examples of these are the famous Tracy-Widom distribution function and the Airy2 process. The objectives of this thesis are threefold: First, we discuss known relations between random matrices and some models in the Kardar-Parisi-Zhang universality class, namely the polynuclear growth model and the totally/partially asymmetric simple exclusion processes. For these models, in the limit of large time t, universality of fluctuations has been previously obtained. We consider the convergence to the limiting distributions and determine the (non-universal) first order corrections, which turn out to be a non-random shift of order t-1/3. Subtracting this deterministic correction, the convergence is then of order t-2/3. We also determine the strength of asymmetry in the exclusion process for which the shift is zero and discuss to what extend the discreteness of the model has an effect on the fitting functions. Second, we focus on the Gaussian Unitary Ensemble and its relation to the totally asymmetric simple exclusion process and discuss the appearance of the Tracy-Widom distribution in the two models. For this, we consider extensions of these systems to triangular arrays of interlacing points, the so-called Gelfand-Tsetlin patterns. We show that the correlation functions for the eigenvalues of the matrix minors for complex Dyson's Brownian motion have, when restricted to increasing times and decreasing matrix dimensions, the same correlation kernel as in the extended interacting particle system under diffusion scaling limit. We also analyze the analogous question for a diffusion on complex sample covariance matrices. Finally, we consider the minor process of Hermitian matrix diffusions with constant diagonal drifts. At any given time, this process is determinantal and we provide an explicit expression for its correlation kernel. This is a measure on Gelfand-Tsetlin patterns that also appears in a generalization of Warren's process, in which Brownian motions have level-dependent drifts. We will also show that this process arises in a diffusion scaling limit from the interacting particle system on Gelfand-Tsetlin patterns with level-dependent jump rates

Finite time corrections in KPZ growth models

We consider some models in the Kardar-Parisi-Zhang universality class, namely the polynuclear growth model and the totally/partially asymmetric simple exclusion process. For these models, in the limit of large time t, universality of fluctuations has been previously obtained. In this paper we consider the convergence to the limiting distributions and determine the (non-universal) first order corrections, which turn out to be a non-random shift of order t^{-1/3} (of order 1 in microscopic units). Subtracting this deterministic correction, the convergence is then of order t^{-2/3}. We also determine the strength of asymmetry in the exclusion process for which the shift is zero. Finally, we discuss to what extend the discreteness of the model has an effect on the fitting functions.Comment: 34 pages, 5 figures, LaTeX; Improved version including shift of PASEP height functio

On the partial connection between random matrices and interacting particle systems

In the last decade there has been increasing interest in the fields of random matrices, interacting particle systems, stochastic growth models, and the connections between these areas. For instance, several objects appearing in the limit of large matrices arise also in the long time limit for interacting particles and growth models. Examples of these are the famous Tracy-Widom distribution functions and the Airy_2 process. The link is however sometimes fragile. For example, the connection between the eigenvalues in the Gaussian Orthogonal Ensembles (GOE) and growth on a flat substrate is restricted to one-point distribution, and the connection breaks down if we consider the joint distributions. In this paper we first discuss known relations between random matrices and the asymmetric exclusion process (and a 2+1 dimensional extension). Then, we show that the correlation functions of the eigenvalues of the matrix minors for beta=2 Dyson's Brownian motion have, when restricted to increasing times and decreasing matrix dimensions, the same correlation kernel as in the 2+1 dimensional interacting particle system under diffusion scaling limit. Finally, we analyze the analogous question for a diffusion on (complex) sample covariance matrices.Comment: 31 pages, LaTeX; Added a section concerning the Markov property on space-like path

Assessment of prognosis by physicians involved in work disability evaluation: A qualitative study.

BACKGROUND:Assessment of prognosis of work functioning is a challenging aspect of work disability evaluations. To gain insight into this process, we conducted a qualitative study to determine the aspects considered and the difficulties, needs and potential solutions affecting the prognosis assessment by physicians performing disability evaluations. METHODS:In-depth, semi-structured individual interviews were conducted with 20 physicians performing disability evaluations for the Dutch social security institute: the national institute for employee benefit schemes. Verbatim transcripts were independently analyzed by two researchers using MAXQDA software until significant themes emerged and data saturation was achieved. RESULTS:The responses that emerged from the interviews were clustered in three primary themes. The first theme was "Aspects considered by physicians in assessing prognosis." When making a prognosis, physicians considered the following medical issues: nature and severity of disease, the role of treatment, course of the disease, external information, and medical evidence. Patient-related issues and physician-related aspects were also distinguished. Patient-related aspects concerned the patients' work perspectives and coping or recovery behavior. Physician-related aspects concerned awareness of the physician's own role and reflection on aspects such as empathy for clients and ethical considerations. The second theme was "Difficulties physicians face in assessing prognosis," which included challenges during the assessment of diseases of a complex or less concrete nature, applying prognostic evidence to the individual, and lack of time when seeking prognostic evidence. The third theme concerned "Needs and solutions" formulated by physicians that facilitated the prognostic assessment. It consisted of continuous education, better collaboration with medical specialists and/or labor experts, and the use of prognostic tools such as checklists, apps or internet applications incorporating evidence on prognosis. CONCLUSIONS:Physicians identified several medical and patient-related aspects that elucidated the prognosis assessment. Given the variety of challenges and the need for further support found in the current study, future research should focus on the development and evaluation of training, tools, and guidelines to improve prognosis assessment by physicians

Modernisation des services publics et management social en France et en Allemagne

En Allemagne comme en France, le service public est confronté au défi de la modernisation sous la pression de multiples facteurs : consolidation des budgets publics, mise en concurrence et dérégulation des services d'intérêt général à l'échelle européenne, évolution des attentes des usagers-clients au regard de la flexibilité et de la qualité des services rendus, nécessité de promouvoir à l'échelon des Etats et des régions un environnement public stimulant pour l'activité économique... Ces changements imposent une rénovation en profondeur des modèles classiques d'organisation de l'action publique et, en tout premier lieu, la mise en œuvre de nouvelles formes de management des ressources humaines. Le présent ouvrage rassemble diverses contributions de chercheurs et responsables français et allemands portant sur la gestion de l'emploi et des compétences, la représentation du personnel et les relations sociales dans la sphère publique. Il en ressort un tableau différencié qui met en évidence les conditions et les modalités très variables selon lesquelles ces grands enjeux de la modernisation de l'Etat sont abordés de part et d'autre du Rhin