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We prove large deviation principles (LDPs) for random matrices in the orthogonal group and Stiefel manifold, determining both the speed and good convex rate functions that are explicitly given in terms of certain log-determinants of…

Probability · Mathematics 2022-11-04 Zakhar Kabluchko , Joscha Prochno

We study the evolution of a random walker on a conservative dynamic random environment composed of independent particles performing simple symmetric random walks, generalizing results of [16] to higher dimensions and more general transition…

This work focuses on quantitative representation of transport in systems with quenched disorder. Explicit mapping of the quenched trap model to continuous time random walk is presented. Linear temporal transformation: $t\to…

Statistical Mechanics · Physics 2017-11-22 Stanislav Burov

We consider the branching random walk drifting to $-\infty$ and we investigate large deviations-type estimates for the first passage time. We prove the corresponding law of large numbers and the central limit theorem.

Probability · Mathematics 2017-09-14 Dariusz Buraczewski , Mariusz Maslanka

We consider a simple random walk (dimension one, nearest neighbour jumps) in a quenched random environment. The goal of this work is to provide sufficient conditions, stated in terms of properties of the environment, under which the Central…

Probability · Mathematics 2007-05-23 I. Ya. Goldsheid

We formulate large deviations principle (LDP) for diffusion pair $(X^\epsilon,\xi^\epsilon)=(X_t^\epsilon,\xi_t^\epsilon)$, where first component has a small diffusion parameter while the second is ergodic Markovian process with fast time.…

Probability · Mathematics 2007-05-23 R. Liptser

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…

Probability · Mathematics 2012-12-12 Lung-Chi Chen , Rongfeng Sun

We investigate the long-term behavior of a random walker evolving on top of the simple symmetric exclusion process (SSEP) at equilibrium, in dimension one. At each jump, the random walker is subject to a drift that depends on whether it is…

Probability · Mathematics 2020-10-28 Marcelo R. Hilário , Daniel Kious , Augusto Teixeira

Consider a random walk among random conductances on $\mathbb{Z}^d$ with $d\geq 2$. We study the quenched limit law under the usual diffusive scaling of the random walk conditioned to have its first coordinate positive. We show that the…

Probability · Mathematics 2013-03-12 Christophe Gallesco , Nina Gantert , Serguei Popov , Marina Vachkovskaia

In this article we show that the empirical measure of certain continuous time random walks satisfies a strong large deviation principle with respect to a topology introduced in~\cite{MV2016} by Mukherjee and Varadhan. This topology is…

Probability · Mathematics 2024-09-04 Dirk Erhard , Tertuliano Franco , Joedson de Jesus Santana

Consider the invariance principle for a random walk with random environment (denoted by $\mu$) in time on $\bfR$ in a weak quenched sense. We show that a sequence of the random probability measures on $\bfR$ generated by a bounded Lipschitz…

Probability · Mathematics 2023-03-14 You Lv , Wenming Hong

Particle approximations for certain nonlinear and nonlocal reaction-diffusion equations are studied using a system of Brownian motions with killing. The system is described by a collection of i.i.d. Brownian particles where each particle is…

Probability · Mathematics 2019-05-01 Amarjit Budhiraja , Wai-Tong Louis Fan , Ruoyu Wu

In this paper, we study small noise asymptotics of Markov-modulated diffusion processes in the regime that the modulating Markov chain is rapidly switching. We prove the joint sample-path large deviations principle for the Markov-modulated…

Probability · Mathematics 2023-02-27 Gang Huang , Michel Mandjes , Peter Spreij

We consider random walks in random environments on Z^d. Under a transitivity hypothesis that is much weaker than the customary ellipticity condition, and assuming an absolutely continuous invariant measure on the space of the environments,…

Probability · Mathematics 2013-02-12 Marco Lenci

Techniques of `dynamic renormalization', developed earlier for undirected percolation and the contact model, are adapted to the setting of directed percolation, thereby obtaining solutions of several problems for directed percolation on…

Probability · Mathematics 2007-05-23 Geoffrey Grimmett , Philipp Hiemer

In this paper, we establish a quenched invariance principle for the random walk on a certain class of infinite, aperiodic, oriented random planar graphs called "T-graphs" [Kenyon-Sheffield04]. These graphs appear, together with the…

Probability · Mathematics 2014-01-15 Benoit Laslier

In his 2003 paper, Varadhan proves the averaged large deviation principle for the mean velocity of a particle taking a nearest-neighbor random walk in a uniformly elliptic i.i.d. environment on $\mathbb{Z}^d$ with $d\geq1$, and gives a…

Probability · Mathematics 2009-08-12 Atilla Yilmaz

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…

Probability · Mathematics 2022-12-07 Yuqiang Li , Qiang Yao

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 zero set whose shape is either a singleton point or a line…

Probability · Mathematics 2025-06-04 Jiaming Chen

A proof is provided of a strong law of large numbers for a one-dimensional random walk in a dynamic random environment given by a supercritical contact process in equilibrium. The proof is based on a coupling argument that traces the…

Probability · Mathematics 2013-03-27 Frank den Hollander , Renato dos Santos