Related papers: Velocity surface disorder of large deviation rate …

The quenched and annealed large deviations of the random walk in random environment are shown to conform on any compact set whenever the level of disorder is sufficiently low. In this work, we show that these two large deviations always…

For a random walk in a uniformly elliptic and i.i.d. environment on $\mathbb Z^d$ with $d \geq 4$, we show that the quenched and annealed large deviations rate functions agree on any compact set contained in the boundary $\partial…

We establish large deviation principles and phase transition results for both quenched and annealed settings of nearest-neighbor random walks with constant drift in random nonnegative potentials on $\mathbb Z^d$. We complement the analysis…

In 2003, Varadhan [V03] developed a robust method for proving quenched and averaged large deviations for random walks in a uniformly elliptic and i.i.d. environment (RWRE) on $\mathbb Z^d$. One fundamental question which remained open was…

We consider a random walk in an i.i.d. random environment on Zd and study properties of its large deviation rate function at the origin. It was proved by Comets, Gantert and Zeitouni in dimension d = 1 in 1999 and later by Varadhan in…

We consider large deviations for nearest-neighbor random walk in a uniformly elliptic i.i.d. environment. It is easy to see that the quenched and the averaged rate functions are not identically equal. When the dimension is at least four and…

Let $(Z_n)_{n\in\N}$ be a $d$-dimensional {\it random walk in random scenery}, i.e., $Z_n=\sum_{k=0}^{n-1}Y(S_k)$ with $(S_k)_{k\in\N_0}$ a random walk in $\Z^d$ and $(Y(z))_{z\in\Z^d}$ an i.i.d. scenery, independent of the walk. The…

We consider random walk with bounded jumps on a hypercubic lattice of arbitrary dimension in a dynamic random environment. The environment is temporally independent and spatially translation invariant. We study the rate functions of the…

Consider a one-dimensional shift-invariant attractive spin-flip system in equilibrium, constituting a dynamic random environment, together with a nearest-neighbor random walk that on occupied sites has a local drift to the right but on…

We study the asymptotic behaviour of a random walk whose evolution is dependent on the state of an itself dynamically evolving environment. In particular, we extend our previous results in [Bethuelsen and V\"ollering, 2016] and prove a…

In this work, we study the large deviation properties of random walk in a random environment on $\mathbb{Z}^d$ with $d\geq1$. We start with the quenched case, take the point of view of the particle, and prove the large deviation principle…

We consider a random walk in a random environment (RWRE) on the strip of finite width $\mathbb{Z} \times \{1,2,\ldots,d\}$. We prove both quenched and averaged large deviation principles for the position and the hitting times of the RWRE.…

We derive properties of the rate function in Varadhan's (annealed) large deviation principle for multidimensional, ballistic random walk in random environment, in a certain neighborhood of the zero set of the rate function. Our approach…

Consider a random walk in a time-dependent random environment on the lattice Zd. Recently, Rassoul-Agha, Seppalainen and Yilmaz [RSY11] proved a general large deviation principle under mild ergodicity assumptions on the random environment…

In this paper we study random walks on dynamical random environments in $1 + 1$ dimensions. Assuming that the environment is invariant under space-time shifts and fulfills a mild mixing hypothesis, we establish a law of large numbers and a…

We derive an annealed large deviation principle for the normalised local times of a continuous-time random walk among random conductances in a finite domain in $\Z^d$ in the spirit of Donsker-Varadhan \cite{DV75}. We work in the interesting…

This thesis concerns the study of random walks in random environments (RWRE). Since there are two levels of randomness for random walks in random environments, there are two different distributions for the random walk that can be studied.…

We take the point of view of the particle in a multidimensional nearest neighbor random walk in random environment (RWRE). We prove a quenched large deviation principle and derive a variational formula for the quenched rate function. Most…

We consider the quenched and the averaged (or annealed) large deviation rate functions $I_q$ and $I_a$ for space-time and (the usual) space-only RWRE on $\mathbb{Z}^d$. By Jensen's inequality, $I_a\leq I_q$. In the space-time case, when…

We consider a bounded step size random walk in an ergodic random environment with some ellipticity, on an integer lattice of arbitrary dimension. We prove a level 3 large deviation principle, under almost every environment, with rate…