Related papers: Large deviations for the one-dimensional Edwards m…
In the framework of Harnack type Dirichlet forms, we prove a large deviation principle for the asymptotics of reversible Markov processes with rate function given by the energy of the paths.
We develop a quantitative large deviations theory for random hypergraphs, which rests on tensor decomposition and counting lemmas under a novel family of cut-type norms. As our main application, we obtain sharp asymptotics for joint upper…
The goal of this article is to establish a central limit theorem for the Euler-Maruyama scheme approximating multidimensional SDEs with elliptic Brownian diffusion, under very mild regularity requirements on the drift coefficients. When the…
Let $W^H=\{W^H(t), t \in \rr\}$ be a fractional Brownian motion of Hurst index $H \in (0, 1)$ with values in $\rr$, and let $L = \{L_t, t \ge 0\}$ be the local time process at zero of a strictly stable L\'evy process $X=\{X_t, t \ge 0\}$ of…
We consider an inhomogeneous Erd\H{o}s-R\'enyi random graph $G_N$ with vertex set $[N] = \{1,\dots,N\}$ for which the pair of vertices $i,j \in [N]$, $i\neq j$, is connected by an edge with probability $r(\tfrac{i}{N},\tfrac{j}{N})$,…
We study large deviations asymptotics for a class of unbounded additive functionals, interpreted as normalized accumulated areas, of one-dimensional Langevin diffusions with sub-linear gradient drifts. Our results provide parametric…
We study the large deviation rate functional for the empirical distribution of independent Brownian particles with drift. In one dimension, it has been shown by Adams, Dirr, Peletier and Zimmer that this functional is asymptotically…
A $\delta$ once-reinforced random walk ($\delta$-ORRW) on connected graph is a self-interacting random walk which moves to its neighbors at each step according to the weights of the edges at that time, where the weights are $1$ on edges…
In this article, we consider slow-fast McKean-Vlasov stochastic differential equations driven by Brownian motions and fractional Brownian motions. We give a definition of the large deviation principle (LDP) on the product space related to…
A particle with internal unobserved states diffusing in a force field will generally display effective advection-diffusion. The drift velocity is proportional to the mobility averaged over the internal states, or effective mobility, while…
Employing large deviation theory, we explore current fluctuations of underdamped Brownian motion for the paradigmatic example of a single particle in a one dimensional periodic potential. Two different approaches to the large deviation…
We are dealing with the validity of a large deviation principle for a class of reaction-diffusion equations with polynomial nonlinearity, perturbed by a Gaussian random forcing. We are here interested in the regime where both the strength…
We prove a large deviation principle (LDP) and a fluctuation theorem (FT) for the entropy production rate (EPR) of the following $d$ dimensional stochastic differential equation \begin{equation*} d X_{t}=AX_{t} d t+\sqrt{Q} d B_{t}…
What does an Erdos-Renyi graph look like when a rare event happens? This paper answers this question when p is fixed and n tends to infinity by establishing a large deviation principle under an appropriate topology. The formulation and…
The incidence of rare events in fast-slow systems is investigated via analysis of the large deviation principle (LDP) that characterizes the likelihood and pathway of large fluctuations of the slow variables away from their mean behavior --…
We prove a sample path large deviation principle (LDP) with sub-linear speed for unbounded functionals of certain Markov chains induced by the Lindley recursion. The LDP holds in the Skorokhod space $\mathbb{D}[0,T]$ equipped with the…
This paper is devoted to the problem of sample path large deviations for multidimensional queueing models with feedback. We derive a new version of the contraction principle where the continuous map is not well-defined on the whole space:…
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.
We calculate the large deviations for the length of the longest alternating subsequence and for the length of the longest increasing subsequence in a uniformly random permutation that avoids a pattern of length three. We treat all six…
We study a class of reflected McKean-Vlasov diffusions over a convex domain with self-stabilizing coefficients. This includes coefficients that do not satisfy the classical Wasserstein Lipschitz condition. Further, the process is…