Related papers: Limit theorems for weighted Bernoulli random field…
The theory of random matrices contains many central limit theorems. We have central limit theorems for eigenvalues statistics, for the log-determinant and log-permanent, for limiting distribution of individual eigenvalues in the bulk, and…
We obtain a Bernstein-type inequality for sums of Banach-valued random variables satisfying a weak dependence assumption of general type and under certain smoothness assumptions of the underlying Banach norm. We use this inequality in order…
A sequential importance sampling algorithm is developed for the distribution that results when a matrix of independent, but not identically distributed, Bernoulli random variables is conditioned on a given sequence of row and column sums.…
We derive both Azuma-Hoeffding and Burkholder-type inequalities for partial sums over a rectangular grid of dimension $d$ of a random field satisfying a weak dependency assumption of projective type: the difference between the expectation…
This paper considers the asymptotic behaviour of volumes of excursion sets of subordinated Gaussian random fields with (possibly) infinite variance. Actually, we consider integral functionals of such fields and obtain their limiting…
In this paper we study the central limit theorem and its functional form for random fields which are not started from their equilibrium, but rather under the measure conditioned by the past sigma field. The initial class considered is that…
We investigate the realizations of a random Gaussian field on a finite domain of ${\mathbb R}^d$ in the limit where a given linear functional of the field is large. We prove that if its variance is bounded, the field converges uniformly and…
We obtain an almost sure limit theorem for the maximum of nonstationary random fields under some dependence conditions.
The standard central limit theorem with a Gaussian attractor for the sum of independent random variables may lose its validity in presence of strong correlations between the added random contributions. Here, we study this problem for…
In this paper we study the convergence in distribution and the local limit theorem for the partial sums of linear random fields with i.i.d. innovations that have infinite second moment and belong to the domain of attraction of a stable law…
In this paper we prove exponential inequalities (also called Bernstein's inequality) for fractional martingales. As an immediate corollary, we will discuss weak law of large numbers for fractional martingales under divergence assumption on…
This paper studies the asymptotic properties of weighted sums of the form $Z_n=\sum_{i=1}^n a_i X_i$, in which $X_1, X_2, \ldots, X_n$ are i.i.d.~random variables and $a_1, a_2, \ldots, a_n$ correspond to either eigenvalues or singular…
This is an extended version of a series of talks I held at the University of Bochum in 2017 about limit theorems for non-linear functionals of stationary Gaussian random fields. The goal of these talks was to give a fairly detailed…
For functions of independent random variables, various upper and lower variance bounds are revisited in diverse settings. These are then specialized to the Bernoulli, Gaussian, infinitely divisible cases and to Banach space valued random…
We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…
The lowest order quantum corrections to the effective action arising from quantized massive fermion fields in the Randall-Sundrum background spacetime are computed. The boundary conditions and their relation with gauge invariance are…
Bounds for the expected return probability of the delayed random walk on finite clusters of an invariant percolation on transitive unimodular graphs are derived. They are particularly suited for the case of critical Bernoulli percolation…
In this paper, we establish a local limit theorem for linear fields of random variables constructed from independent and identically distributed innovations each with finite second moment. When the coefficients are absolutely summable we do…
We present a general central limit theorem with simple, easy-to-check covariance-based sufficient conditions for triangular arrays of random vectors when all variables could be interdependent. The result is constructed from Stein's method,…
This paper establishes limit theorems and quantitative statistical stability for a class of piecewise partially hyperbolic maps that are not necessarily continuous nor locally invertible. By employing a flexible functional-analytic…