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Infinite queueing systems with tree structure

Lucie Fajfrová (2006)

Kybernetika

We focus on invariant measures of an interacting particle system in the case when the set of sites, on which the particles move, has a structure different from the usually considered set ℤ d . We have chosen the tree structure with the dynamics that leads to one of the classical particle systems, called the zero range process. The zero range process with the constant speed function corresponds to an infinite system of queues and the arrangement of servers in the tree structure is natural in a number...

Large scale behavior of semiflexible heteropolymers

Francesco Caravenna, Giambattista Giacomin, Massimiliano Gubinelli (2010)

Annales de l'I.H.P. Probabilités et statistiques

We consider a general discrete model for heterogeneous semiflexible polymer chains. Both the thermal noise and the inhomogeneous character of the chain (the disorder) are modeled in terms of random rotations. We focus on the quenched regime, i.e., the analysis is performed for a given realization of the disorder. Semiflexible models differ substantially from random walks on short scales, but on large scales a brownian behavior emerges. By exploiting techniques from tensor analysis and non-commutative...

Local order at arbitrary distances in finite-dimensional spin-glass models

Pierluigi Contucci, Francesco Unguendoli (2005)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

For a finite dimensional spin-glass model we prove low temperature local order i.e. the property of concentration of the overlap distribution close to the value 1. The theorem hold for both local observables and for products of observables at arbitrary mutual distance: when the Hamiltonian includes the Edwards-Anderson interaction we prove bond local order, when it includes the random-field interaction we prove site local order.

Localisation for non-monotone Schrödinger operators

Alexander Elgart, Mira Shamis, Sasha Sodin (2014)

Journal of the European Mathematical Society

We study localisation effects of strong disorder on the spectral and dynamical properties of (matrix and scalar) Schrödinger operators with non-monotone random potentials, on the d -dimensional lattice. Our results include dynamical localisation, i.e. exponentially decaying bounds on the transition amplitude in the mean. They are derived through the study of fractional moments of the resolvent, which are finite due to resonance-diffusing effects of the disorder. One of the byproducts of the analysis...

Localisation pour des opérateurs de Schrödinger aléatoires dans L 2 ( ℝ d ) : un modèle semi-classique

Frédéric Klopp (1995)

Annales de l'institut Fourier

Dans L 2 ( ℝ d ) , nous démontrons un résultat de localisation exponentielle pour un opérateur de Schrödinger semi-classique à potentiel périodique perturbé par de petites perturbations aléatoires indépendantes identiquement distribuées placées au fond de chaque puits. Pour ce faire, on montre que notre opérateur, restreint à un intervalle d’énergie convenable, est unitairement équivalent à une matrice aléatoire infinie dont on contrôle bien les coefficients. Puis, pour ce type de matrices, on prouve un résultat...

Localization for Schrödinger operators with Poisson random potential

Abel Klein, Peter Hislop, François Germinet (2007)

Journal of the European Mathematical Society

We prove exponential and dynamical localization for the Schr¨odinger operator with a nonnegative Poisson random potential at the bottom of the spectrum in any dimension. We also conclude that the eigenvalues in that spectral region of localization have finite multiplicity. We prove similar localization results in a prescribed energy interval at the bottom of the spectrum provided the density of the Poisson process is large enough.

Mean-field evolution of fermionic systems

Marcello Porta (2014/2015)

Séminaire Laurent Schwartz — EDP et applications

We study the dynamics of interacting fermionic systems, in the mean-field regime. We consider initial states which are close to quasi-free states and prove that, under suitable assumptions on the inital data and on the many-body interaction, the quantum evolution of the system is approximated by a time-dependent quasi-free state. In particular we prove that the evolution of the reduced one-particle density matrix converges, as the number of particles goes to infinity, to the solution of the time-dependent...

Moderate deviations for a Curie–Weiss model with dynamical external field

Anselm Reichenbachs (2013)

ESAIM: Probability and Statistics

In the present paper we prove moderate deviations for a Curie–Weiss model with external magnetic field generated by a dynamical system, as introduced by Dombry and Guillotin-Plantard in [C. Dombry and N. Guillotin-Plantard, Markov Process. Related Fields 15 (2009) 1–30]. The results extend those already obtained for the Curie–Weiss model without external field by Eichelsbacher and Löwe in [P. Eichelsbacher and M. Löwe, Markov Process. Related Fields 10 (2004) 345–366]. The Curie–Weiss model with...

On quenched and annealed critical curves of random pinning model with finite range correlations

Julien Poisat (2013)

Annales de l'I.H.P. Probabilités et statistiques

This paper focuses on directed polymers pinned at a disordered and correlated interface. We assume that the disorder sequence is a q -order moving average and show that the critical curve of the annealed model can be expressed in terms of the Perron–Frobenius eigenvalue of an explicit transfer matrix, which generalizes the annealed bound of the critical curve for i.i.d. disorder. We provide explicit values of the annealed critical curve for q = 1 and q = 2 and a weak disorder asymptotic in the general case....

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