Related papers: Large and moderate deviations for a $\mathbb{R}^d$…

We consider a branching random walk in time-inhomogeneous random environment, in which all particles at generation $k$ branch into the same random number of particles $\mathcal{L}_{k+1}\ge 2$, where the $\mathcal{L}_k$, $k\in\mathbb{N}$,…

Let $X$ be a L\'evy process with regularly varying L\'evy measure $\nu$. We obtain sample-path large deviations for scaled processes $\bar X_n(t) \triangleq X(nt)/n$ and obtain a similar result for random walks. Our results yield detailed…

Given a supercritical branching random walk $\{Z_n\}_{n\geq 0}$ on $\mathbb{R}$, let $Z_n([y,\infty))$ be the number of particles located in $[y,\infty)\subset\mathbb{R}$ at generation $n$. Let $m$ be the mean of the offspring law of…

This paper investigates the large deviation problem in the sample path space of the nearest-neighbor random walks on regular trees. We establish the sample path large deviation principle for the law of the distance from a nearest random…

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 hypothesis being that the conductances are bounded away from…

We prove large deviations principles in large time, for the Brownian occupation time in random scenery. The random scenery is constant on unit cubes, and consist of i.i.d. bounded variables, independent of the Brownian motion. This model is…

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…

The deviation principles of record numbers in random walk models have not been completely investigated, especially for the non-nearest neighbor cases. In this paper, we derive the asymptotic probabilities of large and moderate deviations…

We consider the branching process in random environment $\{Z_n\}_{n\geq 0}$, which is a~population growth process where individuals reproduce independently of each other with the reproduction law randomly picked at each generation. We…

We revisit the multifractal analysis of $\R^d$-valued branching random walks averages by considering subsets of full Hausdorff dimension of the standard level sets, over each infinite branch of which a quantified version of the…

We establish via a probabilistic approach the quenched invariance principle for a class of long range random walks in independent (but not necessarily identically distributed) balanced random environments, with the transition probability…

Behind the nice unification provided by the notion of the level 2.5 in the field of large deviations for time-averages over a long Markov trajectory, there are nevertheless very important qualitative differences between the meaning of the…

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 a time-continuous branching random walk on a one-dimensional lattice on which there is one center (lattice point) of particle generation, called branching source. The generation of particles in the branching source is described…

We consider a discrete time simple symmetric random walk on Z^d, d>=1, where the path of the walk is perturbed by inserting deterministic jumps. We show that for any time n and any deterministic jumps that we insert, the expected number of…

We consider large deviations for nearest-neighbor random walk in a uniformly elliptic i.i.d. environment on $\mathbb{Z}^d$. There exist variational formulae for the quenched and averaged rate functions $I_q$ and $I_a$, obtained by…

Given an $n$-dimensional random vector $X^{(n)}$ , for $k < n$, consider its $k$-dimensional projection $\mathbf{a}_{n,k}X^{(n)}$, where $\mathbf{a}_{n,k}$ is an $n \times k$-dimensional matrix belonging to the Stiefel manifold…

We present large deviations estimates in the supremum norm for a system of independent random walks superposed with a birth-and-death dynamics evolving on the discrete torus with $N$ sites. The scaling limit considered is the so-called…

We consider a ballistic random walk in an i.i.d. random environment that does not allow retreating in a certain fixed direction. Homogenization and regeneration techniques combine to prove a law of large numbers and an averaged invariance…

We calculate, for a branching random walk $X_n(l)$ to a leaf $l$ at depth $n$ on a binary tree, the positive integer moments of the random variable $\frac{1}{2^{n}}\sum_{l=1}^{2^n}e^{2\beta X_n(l)}$, for $\beta\in\mathbb{R}$. We obtain…