Related papers: Quenched Large Deviations for Simple Random Walks …

We consider a branching random walk on $\mathbb{R}$ with a stationary and ergodic environment $\xi=(\xi_n)$ indexed by time $n\in\mathbb{N}$. Let $Z_n$ be the counting measure of particles of generation $n$. For the case where the…

We show existence of the weak large deviation principle, with a convex rate function, for the renormalized distance from the starting point of irreducible random walks on relatively hyperbolic groups. Under the assumption of finiteness of…

We consider a random walk on a random graph $(V,E)$, where $V$ is the set of open sites under i.i.d. Bernoulli site percolation on the multi-dimensional integer set $\mathbf{Z}^d$, and the transition probabilities of the walk are generated…

We prove the analogue for continuous space-time of the quenched LDP derived in Birkner, Greven and den Hollander (2010) for discrete space-time. In particular, we consider a random environment given by Brownian increments, cut into pieces…

Using the weak convergence approach, we prove the large deviation principle (LDP) for solutions to quasilinear stochastic evolution equations with small Gaussian noise in the critical variational setting, a recently developed general…

We establish annealed and quenched invariance principles for random walks in random conductances lifted to the p-variation rough path topology, allowing for degenerate environments and long-range jumps. Our proof is based on a unified…

In this work we extend the quenched local limit theorem obtained by the authors in [BBDS23]. More precisely, we consider a directed random walk on the backbone of the supercritical oriented percolation cluster in dimensions $d+1$ with…

We recover the Donsker-Varadhan large deviations principle (LDP) for the empirical measure of a continuous time Markov chain on a countable (finite or infinite) state space from the joint LDP for the empirical measure and the empirical flow…

Let $p\in[1,\infty]$. Consider the projection of a uniform random vector from a suitably normalized $\ell^p$ ball in $\mathbb{R}^n$ onto an independent random vector from the unit sphere. We show that sequences of such random projections,…

A quenched large deviation principle for Brownian motion in a non-negative, stationary potential is proved. A sufficient moment condition on the potential is given but unlike the results of Armstrong and Tran (2014) no regularity is…

We study a one-dimensional random walk among random conductances, with unbounded jumps. Assuming the ergodicity of the collection of conductances and a few other technical conditions (uniform ellipticity and polynomial bounds on the tails…

We consider random walks on the support of a random purely atomic measure on $\mathbb{R}^d$ with random jump probability rates. The jump range can be unbounded. The purely atomic measure is reversible for the random walk and stationary for…

We consider a directed random walk on the backbone of the infinite cluster generated by supercritical oriented percolation, or equivalently the space-time embedding of the ``ancestral lineage'' of an individual in the stationary…

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…

Consider a random walk on $\mathbb{Z}^d$ in a translation-invariant and ergodic random environment and starting from the origin. In this short note, assuming that a quenched invariance principle for the opportunely-rescaled walks holds, we…

We prove a quenched central limit theorem for random walks with bounded increments in a randomly evolving environment on $\mathbb{Z}^d$. We assume that the transition probabilities of the walk depend not too strongly on the environment and…

We consider simple random walk on the incipient infinite cluster for the spread-out model of oriented percolation on $Z^d \times Z_+$. In dimensions $d>6$, we obtain bounds on exit times, transition probabilities, and the range of the…

We establish the quenched local limit theorem for reversible random walk on $\Z^d$ (with $d\ge 2$) among stationary ergodic random conductances that permit jumps of arbitrary length. The proof is based on the weak parabolic Harnack…

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…

In this work we determine a process-level Large Deviation Principle (LDP) for a model of interacting particles indexed by a lattice $\mathbb{Z}^d$. The connections are random, sparse and unscaled, so that the system converges in the large…