The effect of disorder on quenched and averaged large deviations for random walks in random environments: Boundary behavior

نویسندگان

چکیده

For a random walk in uniformly elliptic and i.i.d. environment on Zd with d?4, we show that the quenched annealed large deviation rate functions agree any compact set contained boundary ?D?{x?Rd:|x|1=1} of their domain which does not intersect (d?2)-dimensional facets ?D, provided disorder is low enough (depending set). As consequence, obtain simple explicit formula for both such ?D at disorder. In contrast to previous works, our results do assume ballistic behavior are restricted neighborhoods given point (on ?D). addition, complement those Bazaes et al. (2022), where, using different methods, investigate equality interior domain. Finally, general parametrized family environments, strength determines phase transition functions, sense each x??D there exists ?x two x when smaller than disagree it larger. This further reconfirms idea, introduced intimately related functions.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Differing Averaged and Quenched Large Deviations for Random Walks in Random Environments in Dimensions Two and Three

We consider the quenched and averaged (or annealed) large deviation rate functions Iq and Ia for space-time and (the usual) space-only RWRE on Z. By Jensen’s inequality, Ia ≤ Iq. In the space-time case, when d ≥ 3 + 1, Iq and Ia are known to be equal on an open set containing the typical velocity ξo. When d = 1+1, we prove that Iq and Ia are equal only at ξo. Similarly, when d = 2+1, we show th...

متن کامل

Quenched large deviations for multiscale diffusion processes in random environments*

We consider multiple time scales systems of stochastic differential equations with small noise in random environments. We prove a quenched large deviations principle with explicit characterization of the action functional. The random medium is assumed to be stationary and ergodic. In the course of the proof we also prove related quenched ergodic theorems for controlled diffusion processes in ra...

متن کامل

Quenched Free Energy and Large Deviations for Random Walks in Random Potentials

We study quenched distributions on random walks in a random potential on integer lattices of arbitrary dimension and with an arbitrary finite set of admissible steps. The potential can be unbounded and can depend on a few steps of the walk. Directed, undirected and stretched polymers, as well as random walk in random environment, are covered. The restriction needed is on the moment of the poten...

متن کامل

Averaged Large Deviations for Random Walk in a Random Environment

Abstract. In his 2003 paper, Varadhan proves the averaged large deviation principle (LDP) for the mean velocity of a particle performing random walk in a random environment (RWRE) on Z with d ≥ 1, and gives a variational formula for the corresponding rate function Ia. Under the non-nestling assumption (resp. Kalikow’s condition), we show that Ia is strictly convex and analytic on a non-empty op...

متن کامل

Quenched Large Deviations for Random Walk in a Random Environment

We take the point of view of a particle performing random walk with bounded jumps on Z in a stationary and ergodic random environment. We prove the quenched large deviation principle (LDP) for the pair empirical measure of the environment Markov chain. By an appropriate contraction, we deduce the quenched LDP for the mean velocity of the particle and obtain a variational formula for the corresp...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Stochastic Processes and their Applications

سال: 2023

ISSN: ['1879-209X', '0304-4149']

DOI: https://doi.org/10.1016/j.spa.2023.01.003