Related papers: Large Deviation in Continuous Time Random Walks
We consider the linear response of systems modelled by continuous-time random walks (CTRW) and by fractional Fokker-Planck equations under the influence of time-dependent external fields. We calculate the corresponding response functions…
Recent findings suggest that processes such as the electronic energy transfer through the photosynthetic antenna display quantal features, aspects known from the dynamics of charge carriers along polymer backbones. Hence, in modeling energy…
Continuous time random walks are non-Markovian stochastic processes, which are only partly characterized by single-time probability distributions. We derive a closed evolution equation for joint two-point probability density functions of a…
We investigate the Large Deviation behavior in small time of continuous Gaussian processes. We introduce a general procedure allowing to derive Large Deviation Principles in small time starting from the well understood context of Large…
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…
We analyze two models of subdiffusion with stochastic resetting. Each of them consists of two parts: subdiffusion based on the continuous-time random walk (CTRW) scheme and independent resetting events generated uniformly in time according…
In this paper, we study second order fluctuations for the size of the range of a critical branching random walk (BRW) in $\mathbb Z^d$. We consider the BRW with geometric offspring indexed by the Kesten tree, and show that the size of its…
Random walks are used for modeling various dynamics in, for example, physical, biological, and social contexts. Furthermore, their characteristics provide us with useful information on the phase transition and critical phenomena of even…
In this paper we deal with anomalous diffusions induced by Continuous Time Random Walks - CTRW in $\mathbb{R}^n$. A particle moves in $\mathbb{R}^n$ in such a way that the probability density function $u(\cdot,t)$ of finding it in region…
We provide a direct proof of Cram\'er's theorem for geodesic random walks in a complete Riemannian manifold $(M,g)$. We show how to exploit the vector space structure of the tangent spaces to study large deviation properties of geodesic…
The versatility of renewal theory is owed to its abstract formulation. Renewals can be interpreted as steps of a random walk, switching events in two-state models, domain crossings of a random motion, etc. We here discuss a renewal process…
The large deviation function has been known for a long time in the literature for the displacement of the rightmost particle in a branching random walk (BRW), or in a branching Brownian motion (BBM). More recently a number of…
Given a branching random walk $(Z_n)_{n\geq0}$ on $\mathbb{R}$, let $Z_n(A)$ be the number of particles located in interval $A$ at generation $n$. It is well known (e.g., \cite{biggins}) that under some mild conditions, $Z_n(\sqrt…
Giant diffusion, where the diffusion coefficient of a Brownian particle in a periodic potential with an external force is significantly enhanced by the external force, is a non-trivial non-equilibrium phenomenon. We propose a simple…
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…
We study a branching random walk (BRW) taking its values in a random tree $\bT$ (seen as a family tree) with an infinite line of ancestors that is a variant of a supercritical Galton--Watson (GW) tree with offspring distribution $\nu$. The…
We consider a generalization of a one-dimensional stochastic process known in the physical literature as L\'evy-Lorentz gas. The process describes the motion of a particle on the real line in the presence of a random array of marked points,…
Let $G$ be an infinite connected graph with vertex set $V$. Let $\{S_n: n \in \mathbb N_0 \}$ be the simple random walk on $G$ and let $\{ \xi(v) : v \in V \}$ be a collection of i.i.d. random variables which are independent of the random…
We study properties of a non-Markovian random walk $X^{(n)}_l$, $l =0,1,2, >...,n$, evolving in discrete time $l$ on a one-dimensional lattice of integers, whose moves to the right or to the left are prescribed by the…
A Levy walk is a non-Markovian stochastic process in which the elementary steps of the walker consist of motion with constant speed in randomly chosen directions and for a random period of time. The time of flight is chosen from a…