Related papers: Sharp moderate and large deviations for sample qua…

We consider high temperature KMS states for quantum spin systems on a lattice. We prove a large deviation principle for the distribution of empirical averages $\frac{1}{|\Lambda|} \sum_{i\in\Lambda} X_i$, where the $X_i$'s are copies of a…

In this paper, we study law of large numbers, central limit theorem, large and moderate deviations for INAR($\infty$) processes, which as a special case, includes both discrete-time linear Hawkes process and INAR(1) process in the…

Motivated by the study of dependent random variables by coupling with independent blocks of variables, we obtain first sufficient conditions for the moderate deviation principle in its functional form for triangular arrays of independent…

This paper is focused on the moderate-deviations analysis of binary hypothesis testing. The analysis relies on a concentration inequality for discrete-parameter martingales with bounded jumps, where this inequality forms a refinement to the…

We establish the large deviations principle (LDP) and the moderate deviations principle (MDP) and an almost sure version of the central limit theorem (CLT) for the stochastic 3D viscous primitive equations driven by a multiplicative white…

The Moderate Deviations Principle (MDP) is well-understood for sums of independent random variables, worse understood for stationary random sequences, and scantily understood for random fields. Here it is established for splittable random…

We consider large deviations of empirical measures of diffusion processes. In a first part, we present conditions to obtain a large deviations principle (LDP) for a precise class of unbounded functions. This provides an analogue to the…

Let $\{{\bf \mathcal{Z}}_n:n\geq 1\}$ be a sequence of i.i.d. random probability measures. Independently, for each $n\geq 1$, let $(X_{n1},\ldots, X_{nn})$ be a random vector of positive random variables that add up to one. This paper…

Let $(Z_{n})$ be a supercritical branching process in a random environment $\xi $, and $W$ be the limit of the normalized population size $Z_{n}/\mathbb{E}[Z_{n}|\xi ]$. We show large and moderate deviation principles for the sequence $\log…

We consider a system of classical particles confined in a box $\Lambda\subset\mathbb{R}^d$ with zero boundary conditions interacting via a stable and regular pair potential. Based on the validity of the cluster expansion for the canonical…

For measuring the strength of visually-observed subpopulation differences, the Population Difference Criterion is proposed to assess the statistical significance of visually observed subpopulation differences. It addresses the following…

By employing various empirical estimators for the Mutual Information (MI) measure, we calculate and compare the estimates and their confidence intervals for both normal and non-normal bivariate data samples. We find that certain nonlinear…

Let $X_1,\dots, X_n$ be independent and identically distributed random vectors in $\mathbb{R}^d$. Suppose $\mathbb{E} X_1=0$, $\mathrm{Cov}(X_1)=I_d$, where $I_d$ is the $d\times d$ identity matrix. Suppose further that there exist positive…

We develop novel empirical Bernstein inequalities for the variance of bounded random variables. Our inequalities hold under constant conditional variance and mean, without further assumptions like independence or identical distribution of…

Let $(\eta_i)_{i\geq1}$ be a sequence of $\psi$-mixing random variables. Let $m=\lfloor n^\alpha \rfloor, 0< \alpha < 1, k=\lfloor n/(2m) \rfloor,$ and $Y_j = \sum_{i=1}^m \eta_{m(j-1)+i}, 1\leq j \leq k.$ Set $ S_k^o=\sum_{j=1}^{k } Y_j $…

We establish a large deviation theorem for the empirical spectral distribution of random covariance matrices whose entries are independent random variables with mean 0, variance 1 and having controlled forth moments. Some new properties of…

We investigate a Bahadur-Kiefer type representation for the p-th empirical quantile corresponding to a sample of n i.i.d. random variables, when 0<p<1 is a sequence which, in particular, may tend to 0 or 1, i.e. we consider the case of…

We prove a maximal-type large deviation principle for dynamical systems with arbitrarily slow polynomial mixing rates. Also several applications, particularly to billiard systems, are presented.

We propose a consistent estimator of sharp bounds on the variance of the difference-in-means estimator in completely randomized experiments. Generalizing Robins [Stat. Med. 7 (1988) 773-785], our results resolve a well-known identification…

This work studies a two-time-scale functional system given by two jump-diffusions under the scale separation by a small parameter $\varepsilon \rightarrow 0$. The coefficients of the equations that govern the dynamics of the system depend…