Excited random walk.
Finite volume approximation of the effective diffusion matrix : the case of independent bond disorder
Fluctuations of the quenched mean of a planar random walk in an i.i.d. Random environment with forbidden direction.
From the Lifshitz tail to the quenched survival asymptotics in the trapping problem.
Functional CLT for random walk among bounded random conductances.
Geodesics and recurrence of random walks in disordered systems.
Hierarchical pinning model in correlated random environment
We consider the hierarchical disordered pinning model studied in (J. Statist. Phys.66 (1992) 1189–1213), which exhibits a localization/delocalization phase transition. In the case where the disorder is i.i.d. (independent and identically distributed), the question of relevance/irrelevance of disorder (i.e. whether disorder changes or not the critical properties with respect to the homogeneous case) is by now mathematically rather well understood (Probab. Theory Related Fields148 (2010) 159–175,...
Homogenization of locally stationary diffusions with possibly degenerate diffusion matrix
This paper deals with homogenization of second order divergence form parabolic operators with locally stationary coefficients. Roughly speaking, locally stationary coefficients have two evolution scales: both an almost constant microscopic one and a smoothly varying macroscopic one. The homogenization procedure aims to give a macroscopic approximation that takes into account the microscopic heterogeneities. This paper follows [Probab. Theory Related Fields (2009)] and improves this latter work by...
Information recovery from randomly mixed-up message text.
Integrability of exit times and ballisticity for random walks in Dirichlet environment.
Internal DLA in a random environment
Invariance principle for Mott variable range hopping and other walks on point processes
We consider a random walk on a homogeneous Poisson point process with energy marks. The jump rates decay exponentially in the -power of the jump length and depend on the energy marks via a Boltzmann-like factor. The case corresponds to the phonon-induced Mott variable range hopping in disordered solids in the regime of strong Anderson localization. We prove that for almost every realization of the marked process, the diffusively rescaled random walk, with an arbitrary start point, converges to...
Invariance principle for the random conductance model with dynamic bounded conductances
We study a continuous time random walk in an environment of dynamic random conductances in . We assume that the conductances are stationary ergodic, uniformly bounded and bounded away from zero and polynomially mixing in space and time. We prove a quenched invariance principle for , and obtain Green’s functions bounds and a local limit theorem. We also discuss a connection to stochastic interface models.
Large deviations for transient random walks in random environment on a Galton–Watson tree
Consider a random walk in random environment on a supercritical Galton–Watson tree, and let τn be the hitting time of generation n. The paper presents a large deviation principle for τn/n, both in quenched and annealed cases. Then we investigate the subexponential situation, revealing a polynomial regime similar to the one encountered in one dimension. The paper heavily relies on estimates on the tail distribution of the first regeneration time.
Large scale behavior of semiflexible heteropolymers
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...
Limit laws for transient random walks in random environment on
We consider transient random walks in random environment on with zero asymptotic speed. A classical result of Kesten, Kozlov and Spitzer says that the hitting time of the level converges in law, after a proper normalization, towards a positive stable law, but they do not obtain a description of its parameter. A different proof of this result is presented, that leads to a complete characterization of this stable law. The case of Dirichlet environment turns out to be remarkably explicit.
Limit laws of transient excited random walks on integers
We consider excited random walks (ERWs) on ℤ with a bounded number of i.i.d. cookies per site without the non-negativity assumption on the drifts induced by the cookies. Kosygina and Zerner [15] have shown that when the total expected drift per site, δ, is larger than 1 then ERW is transient to the right and, moreover, for δ>4 under the averaged measure it obeys the Central Limit Theorem. We show that when δ∈(2, 4] the limiting behavior of an appropriately centered and scaled excited random...
Limit theorems for one and two-dimensional random walks in random scenery
Random walks in random scenery are processes defined by , where and are two independent sequences of i.i.d. random variables with values in and respectively. We suppose that the distributions of and belong to the normal basin of attraction of stable distribution of index and . When and , a functional limit theorem has been established in (Z. Wahrsch. Verw. Gebiete50 (1979) 5–25) and a local limit theorem in (Ann. Probab.To appear). In this paper, we establish the convergence in...
Limit theorems for one-dimensional transient random walks in Markov environments
Limiting behavior of a diffusion in an asymptotically stable environment