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We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite dimensional Euclidean spaces and bounded functional spaces. Such a generalization…
We study systems of particles on a line which have a maximum, are locally finite and evolve with independent increments. ``Quasi-stationary states'' are defined as probability measures, on the \sigma-algebra generated by the gap variables,…
Broadly distributed random variables with a power-law distribution $f(m) \sim m^{-(1+\alpha)}$ are known to generate condensation effects, in the sense that, when the exponent $\alpha$ lies in a certain interval, the largest variable in a…
The paper deals with studying a connection of the Littlewood--Offord problem with estimating the concentration functions of some symmetric infinitely divisible distributions. It is shown that the values at zero of the concentration…
Exponential averages that appear in integral fluctuation theorems can be recast as a sum over moments of thermodynamic observables. We use two examples to show that such moment series can exhibit non-uniform convergence in certain singular…
It is well known that in a small P\'olya urn, i.e., an urn where second largest real part of an eigenvalue is at most half the largest eigenvalue, the distribution of the numbers of balls of different colours in the urn is asymptotically…
We present the fundamentals of a measure transport approach to sampling. The idea is to construct a deterministic coupling---i.e., a transport map---between a complex "target" probability measure of interest and a simpler reference measure.…
We give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein's inequality from sums to more general functions, whose variation in any argument does not depend too much on the…
This article considers a class of disordered mean-field combinatorial optimization problems. We focus on the Gibbs measure, where the inverse temperature does not vary with the size of the graph and the edge weights are sampled from a…
An atomic random complex measure defined on the unit disk with Normally distributed moments is considered. An approximation to the distribution of the zeros of its Cauchy transform is computed. Implications of this result for solving…
General sufficient conditions are given for absolute continuity and convergence in variation of the distributions of the unctionals on a probability space, generated by a Poisson point measure. The phase space of the Poisson point measure…
We explore the asymptotic distributions of sequences of integer-valued additive functions defined on the symmetric group endowed with the Ewens probability measure as the order of the group increases. Applying the method of factorial…
We study the question, ``For which reals $x$ does there exist a measure $\mu$ such that $x$ is random relative to $\mu$?'' We show that for every nonrecursive $x$, there is a measure which makes $x$ random without concentrating on $x$. We…
A permutation $\sigma$ describing the relative orders of the first $n$ iterates of a point $x$ under a self-map $f$ of the interval $I=[0,1]$ is called an \emph{order pattern}. For fixed $f$ and $n$, measuring the points $x\in I$ (according…
This paper is concerned with the study of the consistency of a variational method for probability measure quantization, deterministically realized by means of a minimizing principle, balancing power repulsion and attraction potentials. The…
In this article we recover the distribution function (and possible density) of an arbitrary random variable that is subject to an additive measurement error. This problem is also known as deconvolution and has a long tradition in…
Skewness measures can be used to measure the level of asymmetry of a distribution. Given the prevalence of statistical methods that assume underlying symmetry, and also the desire for symmetry in order to make meaningful judgements for…
This paper contributes to the study of the free additive convolution of probability measures. It shows that under some conditions, if measures $\mu_i$ and $\nu_i, i=1,2$, are close to each other in terms of the L\'{e}vy metric and if the…
The martingale method is used to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the…
The problem is sequence prediction in the following setting. A sequence x1,..., xn,... of discrete-valued observations is generated according to some unknown probabilistic law (measure) mu. After observing each outcome, it is required to…