Related papers: Non-central limit theorem for non-linear functiona…
Fix an integer $p\geq 1$ and refer to it as the number of growing domains. For each $i\in\{1,\ldots,p\}$, fix a compact subset $D_i\subseteq\mathbb R^{d_i}$ where $d_1,\ldots,d_p\ge 1$. Let $d= d_1+\dots+d_{p}$ be the total underlying…
We provide a functional central limit theorem for a broad class of smooth functions for possibly noncausal multivariate linear processes with time-varying coefficients. Since the limiting processes depend on unknown quantities, we propose a…
In literature, the central limit theorems for the product of sums of various random variables have studied. The purpose of this note is to show that this kind of results are corollary of the invariance principle.
In this note, we prove a quenched functional central limit theorem for a biased random walk on a supercritical Galton-Watson tree with leaves. This extends a result of Peres and Zeitouni (2008) where the case without leaves is considered. A…
Lacunary function systems of type $(f(M_nx))_{n\geq 1}$ for periodic functions $f$ and sequences of fast-growing matrices $(M_n)_{n\geq 1}$ exhibit many properties of independent random variables like satisfying the Central Limit Theorem or…
We derive novel anti-concentration bounds for the difference between the maximal values of two Gaussian random vectors across various settings. Our bounds are dimension-free, scaling with the dimension of the Gaussian vectors only through…
The field of analytic combinatorics is dedicated to the creation of effective techniques to study the large-scale behaviour of combinatorial objects. Although classical results in analytic combinatorics are mainly concerned with univariate…
In this paper we will prove a functional central limit theorems for "nonconventional" sums indexed by polynomial arrays.
We prove a non-asymptotic central limit theorem for vector-valued martingale differences using Stein's method, and use Poisson's equation to extend the result to functions of Markov Chains. We then show that these results can be applied to…
In this paper, we derive asymptotic results for L^1-Wasserstein distance between the distribution function and the corresponding empirical distribution function of a stationary sequence. Next, we give some applications to dynamical systems…
The paper introduces a non-linear version of the process convolution formalism for building covariance functions for multi-output Gaussian processes. The non-linearity is introduced via Volterra series, one series per each output. We…
In this paper, we prove a conditional limit theorem for independent not necessarily identically distributed random variables. Namely, we obtain the asymptotic distribution of a large number of them given the sum.
In a series of previous articles by the author, it was shown that one could effectively give a variational formulation to non-conservative mechanical systems, as well as ones that subject to non-holonomic constraints by starting with the…
In this talk I first review at an elementary level a selection of central limit theorems, including some lesser known cases, for sums and maxima of uncorrelated and correlated random variables. I recall why several of them appear in…
This paper provides refined versions of some known functional central limit theorems for conditional Poisson sampling which are more suitable for applications. The theorems presented in this paper are generalizations of some results that…
Consider the random variable $\mathrm{Tr}( f_1(W)A_1\dots f_k(W)A_k)$ where $W$ is an $N\times N$ Hermitian Wigner matrix, $k\in\mathbb{N}$, and choose (possibly $N$-dependent) regular functions $f_1,\dots, f_k$ as well as bounded…
We prove a central limit theorem for non-commutative random variables in a von Neumann algebra with a tracial state: Any non-commutative polynomial of averages of i.i.d. samples converges to a classical limit. The proof is based on a…
We find a sufficient condition under which a central limit theorem for a stationary linear process is quenched. We find a stationary linear process szatisfying the Maxwell-Woodroofe condition for which the variances of partial sums are…
We establish a general criterion for the positivity of the variance of a chaotic component of local functionals of stationary vector-valued Gaussian fields. This criterion is formulated in terms of the spectral properties of the covariance…
This note presents some central limit theorems for the eigenvalue counting function of Wigner matrices in the form of suitable translations of results by Gustavsson and O'Rourke on the limiting behavior of eigenvalues inside the bulk of the…