Related papers: Large Deviation Principles for countable Markov sh…

Following work of Mehrdad and Zhu and of Liu, we prove a large deviation principle for a broad class of integer-valued additive functions defined over abelian monoids. As a corollary, we obtain a large deviation principle for a generalized…

This work is concerned with the large deviation principle for a family of slow-fast systems perturbed by infinite-dimensional mixed fractional Brownian motion with Hurst parameter $H\in(\frac12,1)$. We adopt the weak convergence method…

We consider a non-stationary Cox-Ingersoll-Ross process. We establish a sharp large deviation principle for the maximum likelihood estimator of its drift parameter.

We derive a large deviation principle for families of random variables in the basin of attraction of spectrally positive stable distributions by proving a uniform version of the Tauberian theorem for Laplace-Stieltjes transforms. The main…

We prove the almost sure invariance principle with rate $o(n^{\varepsilon})$ for every $\varepsilon > 0$ for H\"older continuous observables on nonuniformly expanding and nonuniformly hyperbolic transformations with exponential tails.…

Markov processes restarted or reset at random times to a fixed state or region in space have been actively studied recently in connection with random searches, foraging, and population dynamics. Here we study the large deviations of…

In this document, we aim to gather various results related to a compositional/categorical approach to rigorous Statistical Mechanics. Rigorous Statistical Mechanics is centered on the mathematical study of statistical systems. Central…

Conditional independence and Markov properties are powerful tools allowing expression of multidimensional probability distributions by means of low-dimensional ones. As multidimensional possibilistic models have been studied for several…

We derive the explicit form of the rate function for semi-Markov processes. Here, the "random time change trick" plays an essential role. Also, by exploiting the contraction principle of the large deviation theory to the explicit form, we…

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 $r(\tfrac{i}{N},\tfrac{j}{N})$,…

Let $(X,T)$ and $(Y,S)$ be two subshifts so that $Y$ is a factor of $X$. For any asymptotically sub-additive potential $\Phi$ on $X$ and $\ba=(a,b)\in\R^2$ with $a>0$, $b\geq 0$, we introduce the notions of $\ba$-weighted topological…

We prove large deviation principles (LDPs) for full chordal, radial, and multichordal SLE(0+) curves parameterized by capacity. The rate function is given by the appropriate variant of the Loewner energy. There are two key novelties in the…

Let $\Delta^o$ be a finite set and, for each probability measure $m$ on $\Delta^o$, let $G(m)$ be a transition probability kernel on $\Delta^o$. Fix $x_0 \in \Delta^o$ and consider the chain $\{X_n, \; n \in \mathbb{N}_0\}$ of…

We derive a large deviation principle for the empirical measure of zeros of random polynomials with i.i.d. exponential coefficients.

The aim of this paper is to improve the large deviation principle for the number of descents in a random permutation by establishing a sharp large deviation principle of any order. We shall also prove a sharp large deviation principle of…

For a dynamical system, we study the set of points $\cal W$ whose orbit approximates any chosen point at certain specified rates. Our basic setting is that of left shift acting on topological Markov chains endowed with a local weak Gibbs…

The final proportion of ignorants in the classical Maki--Thompson rumour model is known to satisfy the law of large numbers, the central limit theorem, and the large deviation principle. In this note, we establish the corresponding moderate…

We examine two analytical characterisation of the metastable behavior of a Markov chain. The first one expressed in terms of its transition probabilities, and the second one in terms of its large deviations rate functional. Consider a…

In recent papers it has been demonstrated that sampling a Gibbs distribution from an appropriate time-irreversible Langevin process is, from several points of view, advantageous when compared to sampling from a time-reversible one. Adding…

This paper focuses on systems of nonlinear second-order stochastic differential equations with multi-scales. The motivation for our study stems from mathematical physics and statistical mechanics, for examples, Langevin dynamics and…