Related papers: Polynomial Tail Decay for Stationary Measures

For differentiable dynamical systems with dominated splittings, we give upper estimates on the measure-theoretic tail entropy in terms of Lyapunov exponents. As our primary application, we verify the upper semi-continuity of metric entropy…

In this note we prove bounds on the upper and lower probability tails of sums of independent geometric or exponentially distributed random variables. We also prove negative results showing that our established tail bounds are asymptotically…

If the Euclidean norm is strongly concentrated with respect to a measure, the average distribution of an average marginal of this measure has Gaussian asymptotics that captures tail behaviour. If the marginals of the measure have…

We study the stationary measures for variants of the Porous Medium Model in dimension 1. These are exclusion processes that belong to the class of kinetically constrained models, in which an exchange can occur between $x$ and $x+1$ only if…

In this paper we propose a framework that enables the study of large deviations for point processes based on stationary sequences with regularly varying tails. This framework allows us to keep track not of the magnitude of the extreme…

Let $\Psi_1,\Psi_2,...$ be a sequence of i.i.d. random Lipschitz functions on a complete separable metric space with unbounded metric $d$ and forward iterations $X_n$. Suppose that $X_n$ has a stationary distribution. We study the…

This paper studies the light-tailed asymptotics of the stationary tail probability vectors of a Markov chain of M/G/1 type. Almost all related studies have focused on the typical case, where the transition block matrices in the non-boundary…

We derive sufficient conditions for asymptotic and monotone exponential decay in mean square of solutions of the geometric Brownian motion with delay. The conditions are written in terms of the parameters and are explicit for the case of…

We develop an early-warning signal for bifurcations of one-dimensional random difference equations with additive bounded noise, based on the asymptotic behaviour of the stationary density near a boundary of its support. We demonstrate the…

The goal of this paper is to investigate the tools of extreme value theory originally introduced for discrete time stationary stochastic processes (time series), namely the tail process and the tail measure, in the framework of continuous…

This work develops a methodology for analyzing large-deviation lower tails associated with geometric functionals computed on a homogeneous Poisson point process. The technique applies to characteristics expressed in terms of stabilizing…

Consider the partition function of a directed polymer in an IID field. We assume that both tails of the negative and the positive part of the field are at least as light as exponential. It is a well-known fact that the free energy of the…

We compute tail contributions to the conservative dynamics of a generic self-gravitating system, for every multipole order, of either electric and magnetic parity. Such contributions arise when gravitational radiation is backscattered by…

We present a new technique to obtain polynomial decay estimates for the matrix coefficients of unitary operators. Our approach, based on commutator methods, applies to nets of unitary operators, unitary representations of topological…

We study the behavior of the tail of a measure $\mu^{\boxtimes t}$, where $\boxtimes t$ is the $t$-fold free multiplicative convolution power for $t\geq 1$. We focus on the case where $\mu$ is a probability measure on the positive half-line…

A network belongs to the monotone separable class if its state variables are homogeneous and monotone functions of the epochs of the arrival process. This framework contains several classical queueing network models, including generalized…

Let $P$ be a polynomial of degree $d$ in independent Bernoulli random variables which has zero mean and unit variance. The Bonami hypercontractivity bound implies that the probability that $|P| > t$ decays exponentially in $t^{2/d}$.…

We investigate a way of comparing and classifying tails of random variables. Our approach extends the notion of classical indices, such as exponential and moment indices, which are widely used measuring heaviness of tail functions. A…

We consider the energy of a randomly charged polymer. We assume that only charges on the same site interact pairwise. We study the lower tails of the energy, when averaged over both randomness, in dimension three or more. As a corollary, we…

We derive upper and lower bounds for the upper and lower tails of the O'Connell-Yor polymer of the correct order of magnitude via probabilistic and geometric techniques in the moderate deviations regime. The inputs of our work are an…