Random walks in Dirichlet environment: an overview

C Sabot, L Tournier - Annales de la Faculté des sciences …, 2017‏ - afst.centre-mersenne.org
Random Walks in Dirichlet Environment (RWDE) correspond to Random Walks in Random
Environment (RWRE) on Zd where the transition probabilities are iid at each site with a …

Variance decay for functionals of the environment viewed by the particle

JC Mourrat - Annales de l'IHP Probabilités et statistiques, 2011‏ - numdam.org
For the random walk among random conductances, we prove that the environment viewed
by the particle converges to equilibrium polynomially fast in the variance sense, our main …

A quenched invariance principle for non-elliptic random walk in iid balanced random environment

N Berger, JD Deuschel - Probability Theory and Related Fields, 2014‏ - Springer
We consider a random walk on Z^ d,\d ≥ 2, in an iid balanced random environment, that is a
random walk for which the probability to jump from x ∈ Z^ d to nearest neighbor x+ e is the …

Quenched and averaged large deviations for random walks in random environments: The impact of disorder

R Bazaes, C Mukherjee, AF Ramírez… - The Annals of Applied …, 2023‏ - projecteuclid.org
In 2003, Varadhan (Comm. Pure Appl. Math. 56 (2003) 1222–1245) developed a robust
method for proving quenched and averaged large deviations for random walks in a …

Almost sure functional central limit theorem for ballistic random walk in random environment

F Rassoul-Agha, T Seppäläinen - Annales de l'IHP Probabilités et …, 2009‏ - numdam.org
We consider a multidimensional random walk in a product random environment with
bounded steps, transience in some spatial direction, and high enough moments on the …

Large deviations of quenched and annealed random walk in mixing random environment

J Chen - arxiv preprint arxiv:2409.06581, 2024‏ - arxiv.org
In this work, we establish the existence of large deviation principles of random walk in
strongly mixing environments. The quenched and annealed rate functions have the same …

Local limit theorem and equivalence of dynamic and static points of view for certain ballistic random walks in iid environments

N Berger, M Cohen, R Rosenthal - 2016‏ - projecteuclid.org
In this work, we discuss certain ballistic random walks in random environments on Z^d, and
prove the equivalence between the static and dynamic points of view in dimension d\geq4 …

Random Dirichlet environment viewed from the particle in dimension

C Sabot - 2013‏ - projecteuclid.org
We consider random walks in random Dirichlet environment (RWDE), which is a special type
of random walks in random environment where the exit probabilities at each site are iid …

Limit theorem for subdiffusive random walk in Dirichlet random environment in dimension

A Perrel - arxiv preprint arxiv:2404.06502, 2024‏ - arxiv.org
We consider random walk in Dirichlet random environment in ${\mathbf {Z}^ d, d\ge 3} $,
which corresponds to the case where the environment is constructed from iid transition …

Equality of averaged and quenched large deviations for random walks in random environments in dimensions four and higher

A Yilmaz - Probability theory and related fields, 2011‏ - Springer
We consider large deviations for nearest-neighbor random walk in a uniformly elliptic iid
environment. It is easy to see that the quenched and the averaged rate functions are not …