相关论文: Concentration inequalities for random fields via c…
Consider an ergodic stationary random field $A$ on the ambient space $\mathbb R^d$. In order to establish concentration properties for nonlinear functions $Z(A)$, it is standard to appeal to functional inequalities like Poincar\'e or…
Correlation inequalities have played an essential role in the analysis of ferromagnetic models but have not been established in spin glass models. In this study, we obtain some correlation inequalities for the Ising models with quenched…
The aim of this paper is to establish Hoeffding and Bernstein type concentration inequalities for weighted sums of exchangeable random variables. A special case is the i.i.d. setting, where random variables are sampled independently from…
This article is concerned with the fluctuations and the concentration properties of a general class of discrete generation and mean field particle interpretations of nonlinear measure valued processes. We combine an original stochastic…
Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering ferromagnetism, combinatorial optimization, protein folding, stock market dynamics, and social dynamics.…
We present a proof of the concentration inequality for a discrete random surface model, where the underlying potential is perturbed by an additive random potential. The proof is based on annealing the random potential, and follows the…
New Vapnik and Chervonenkis type concentration inequalities are derived for the empirical distribution of an independent random sample. Focus is on the maximal deviation over classes of Borel sets within a low probability region. The…
We propose a novel approach to concentration for non-independent random variables. The main idea is to ``pretend'' that the random variables are independent and pay a multiplicative price measuring how far they are from actually being…
We obtain large and moderate deviation estimates, as well as concentration inequalities, for a class of nonuniformly expanding maps with stretched exponential decay of correlations. In the large deviation regime, we also exhibit examples…
This paper presents compact notations for concentration inequalities and convenient results to streamline probabilistic analysis. The new expressions describe the typical sizes and tails of random variables, allowing for simple operations…
We study the concentration phenomenon for discrete-time random dynamical systems with an unbounded state space. We develop a heuristic approach towards obtaining exponential concentration inequalities for dynamical systems using an entirely…
We generalise disagreement percolation to Gibbs point processes of balls with varying radii. This allows to establish the uniqueness of the Gibbs measure and exponential decay of pair correlations in the low activity regime by comparison…
We study the approximation of non-negative multi-variate couplings in the uniform norm while matching given single-variable marginal constraints.
Initially motivated by the study of the non-asymptotic properties of non-parametric tests based on permutation methods, concentration inequalities for uniformly permuted sums have been largely studied in the literature. Recently, Delyon et…
We consider a Boolean model $Z$ driven by a Poisson particle process $\eta$ on a metric space $\mathbb{Y}$. We study the random variable $\rho(Z)$, where $\rho$ is a (deterministic) measure on $\mathbb{Y}$. Due to the interaction of…
This work improves the existing central limit theorems (CLTs) for geometric functionals of Gibbs processes in three aspects. First, we derive a CLT for weakly stabilizing functionals, thereby improving on the previously used assumption of…
We show that the mixing times of random walks on compact groups can be used to obtain concentration inequalities for the respective Haar measures. As an application, we derive a concentration inequality for the empirical distribution of…
Concentration bounds for non-product, non-Haar measures are fairly recent: the first such result was obtained for contracting Markov chains by Marton in 1996 via the coupling method. The work that followed, with few exceptions, also used…
If a random variable is not exponentially integrable, it is known that no concentration inequality holds for an infinite sequence of independent copies. Under mild conditions, we establish concentration inequalities for finite sequences of…
The replicated field theory of the random field Ising model involves the couplings of replicas of different indices. The resulting correlation functions involve a superposition of different types of long distance behaviours. However the…