Study of the Iterations of a Mapping Associated to a Spin Glass Model
Subdiffusive behavior of random walk on a random cluster
Supercritical self-avoiding walks are space-filling
In this article, we consider the following model of self-avoiding walk: the probability of a self-avoiding trajectory between two points on the boundary of a finite subdomain of is proportional to . When is supercritical (i.e. where is the connective constant of the lattice), we show that the random trajectory becomes space-filling when taking the scaling limit.
Sur la mécanique statistique d'une particule brownienne sur le tore
Sur le modèle d'Heisenberg
Sur le mouvement d'une particule lourde soumise à des collisions dans un système infini de particules légères
Sur le nombre de points visités par une marche aléatoire sur un amas infini de percolation
On s’intéresse à une marche aléatoire simple sur un amas infini issu d’un processus de percolation surcritique sur les arêtes de de loi . On montre que la transformée de Laplace du nombre de points visités au temps , noté , a un comportement similaire au cas où la marche évolue dans . Plus précisément, on établit que pour tout , il existe des constantes , telles que pour presque toute réalisation de la percolation telle que l’origine appartienne à l’amas infini et pour assez grand,Le...
Sur les inégalités FKG
Sur l'utilisation de processus de Markov dans le modèle d'Ising : attractivité et couplage
Survival probability approach to the relaxation of a macroscopic system in the defect-diffusion framework
The main objective of this paper is to present a new probabilistic model underlying the universal relaxation laws observed in many fields of science where we associate the survival probability of the system's state with the defect-diffusion framework. Our approach is based on the notion of the continuous-time random walk. To derive the properties of the survival probability of a system we explore the limit theorems concerning either the summation or the extremes: maxima and minima. The forms of...
Système de processus auto-stabilisants [Book]
Systèmes de particules et mesures-martingales : un théorème de propagation du chaos
Systemic risk through contagion in a core-periphery structured banking network
We contribute to the understanding of how systemic risk arises in a network of credit-interlinked agents. Motivated by empirical studies we formulate a network model which, despite its simplicity, depicts the nature of interbank markets better than a symmetric model. The components of a vector Ornstein-Uhlenbeck process living on the nodes of the network describe the financial robustnesses of the agents. For this system, we prove a LLN for growing network size leading to a propagation of chaos result....
Tagged particle limit for a Fleming-Viot type system.
Test for submodel in Gibbs-Markov binary random sequence
The Aizenman-Sims-Starr and Guerra's schemes for the SK model with multidimensional spins.
The asymmetric simple exclusion model with multiple shocks
The atomic and molecular nature of matter.
The purpose of this article is to show that electrons and protons, interacting by Coulomb forces and governed by quantum statistical mechanics at suitable temperature and density, form a gas of Hydrogen atoms or molecules.
The best bounds in a theorem of Russell Lyons.
The center of mass of the ISE and the Wiener index of trees.