Related papers: Moderate deviations for the chemical distance in B…

This article is concerned with moderate deviation principles of a general class of mean eld type interacting particle models. We discuss functional moderate deviations of the occupation measures for both the strong -topology on the space of…

We consider the Gaussian free field $\varphi$ on $\mathbb{Z}^d$ for $d \geq 3$ and study the level sets $\{\varphi \geq h \}$ in the percolating regime. We prove upper and lower bounds for the probability that the chemical distance is much…

We use the Stein-Chen method to prove new explicit inequalities for the total variation, Wasserstein and local distances between the distribution of a random diagonal sum of a Bernoulli matrix and a Poisson distribution. Approximation…

In this paper, we are concerned with obtaining distribution-free concentration inequalities for mixture of independent Bernoulli variables that incorporate a notion of variance. Missing mass is the total probability mass associated to the…

We investigate the first passage time t_{j,N} to a given chemical or Euclidean distance of the first j of a set of N>>1 independent random walkers all initially placed on a site of a disordered medium. To solve this order-statistics problem…

We present a permutation-invariant distance between atomic configurations, defined through a functional representation of atomic positions. This distance enables to directly compare different atomic environments with an arbitrary number of…

We prove that the variance of the passage time from the origin to a point x in first-passage percolation on Z^d is sublinear in the distance to x when d \geq 2, obeying the bound Cx/(log x), under minimal assumptions on the edge-weight…

We consider a variant of the continuous and discrete Ulam-Hammersley problems: we study the maximal length of an increasing path through a Poisson point process (or a Bernoulli point process) with the restriction that there must be minimal…

Moderate deviation principles for empirical measure processes associated with weakly interacting Markov processes are established. Two families of models are considered: the first corresponds to a system of interacting diffusions whereas…

We consider data transmission across discrete memoryless channels (DMCs) using variable-length codes with feedback. We consider the family of such codes whose rates are $\rho_N$ below the channel capacity $C$, where $\rho_N$ is a positive…

Consider the extreme value of a Bernoulli random walk on the one-dimensional integer lattice, with reflection at 0, over a finite discrete time interval. Only the asymmetric (biased) case is discussed. Asymptotic mean/variance results are…

This paper addresses to the problem of finding the (minimum) Euclidean distance between two linear varieties. This problem is, usually, solved minimising a target function. We propose a novel approach: to use the Moore-Penrose generalised…

Motivated by an intention to apply partial wave analysis to systems containing photons, we construct eigenvectors of the distance of separation between two photons. A choice is made that makes the case of two photons most closely resemble…

We obtain moderate deviations theorems and exponential (Bernstein type) concentration inequalities for "nonconventional" sums of the form $S_N=\sum_{n=1}^N (F(\xi_{q_1(n)},\xi_{q_2(n)},...,\xi_{q_\ell(n)})-\bar F)$.

We study the shape fluctuation in the first passage percolation on $\mathbb{Z}^d$. It is known that it diverges when the distribution obeys Bernoulli in [Yu Zhang. The divergence of fluctuations for shape in first passage percolation.…

Let $\{X, X_{n}; n \geq 1\}$ be a sequence of i.i.d. non-degenerate real-valued random variables with $\mathbb{E}X^{2} < \infty$. Let $S_{n} = \sum_{i=1}^{n} X_{i}$, $n \geq 1$. Let $g(\cdot): ~[0, \infty) \rightarrow [0, \infty)$ be a…

Marginal Fermi liquid was originally introduced as a phenomenological description of the cuprates in a part of the metallic doping range which appears to be governed by fluctuations due to a quantum-critical point. An essential result due…

We analyse the asymptotic behaviour of the probability of observing the expected number of successes at each stage of a sequence of nested Bernoulli trials. Our motivation is the attempt to give a genuinely frequentist interpretation to the…

We derive moderate deviation principles for the trajectory of the empirical magnetization of the standard Curie-Weiss model via a general analytic approach based on convergence of generators and uniqueness of viscosity solutions for…

We investigate long-time behaviors of empirical measures associated with subordinated Dirichlet diffusion processes on a compact Riemannian manifold $M$ with boundary $\partial M$ to some reference measure, under the quadratic Wasserstein…