Related papers: A central limit theorem for the two-sided descent …

The classic central limit theorem and $\alpha$-stable distributions play a key role in probability theory, and also in Boltzmann-Gibbs (BG) statistical mechanics. They both concern the paradigmatic case of probabilistic independence of the…

Our main results are quantitative bounds in the multivariate normal approximation of centred subgraph counts in random graphs generated by a general graphon and independent vertex labels. We are interested in these statistics because they…

We prove the Central Limit Theorem for the number of eigenvalues near the spectrum edge for hermitian ensembles of random matrices. To derive our results, we use a general theorem, essentially due to Costin and Lebowitz, concerning the…

A central limit theorem for the integrated squared error of the directional-linear kernel density estimator is established. The result enables the construction and analysis of two testing procedures based on squared loss: a nonparametric…

Suppose that $\{X_t,\,t\ge0\}$ is a non-stationary Markov process, taking values in a Polish metric space $E$. We prove the law of large numbers and central limit theorem for an additive functional of the form $\int_0^T\psi(X_s)ds$,…

In this work, we obtain the central limit theorem for fluctuations of Young diagrams around their limit shape in the bulk of the "spectrum" of partitions of a large integer n (under the Plancherel measure). More specifically, we show that,…

We prove a central limit theorem for the Horvitz-Thompson estimator based on the Gram-Schmidt Walk (GSW) design, recently developed in Harshaw et al.(2022). In particular, we consider the version of the GSW design which uses randomized…

For Dirichlet series roughly of the type $Z(s, w) = sum_d L(s, chi_d) d^{-w}$ the subconvexity bound $Z(s, w) \ll (sw(s+w))^{1/6+\varepsilon}$ is proved on the critical lines $\Re s = \Re w = 1/2$. The convexity bound would replace 1/6 with…

We consider supercritical branching random walks on transitive graphs and we prove a law of large numbers for the mean displacement of the ensemble of particles, and a Stam-type central limit theorem for the empirical distributions, thus…

We establish central limit theorems for an action of a group G on a hyperbolic space X with respect to the counting measure on a Cayley graph of G. Our techniques allow us to remove the usual assumptions of properness and smoothness of the…

Unlike classical simple random walks, one-dimensional random walks in random environments (RWRE) are known to have a wide array of potential limiting distributions. Under certain assumptions, however, it is known that CLT-like limiting…

Wald-type tests are convenient because they allow one to test a wide array of linear and nonlinear restrictions from a single unrestricted estimator; we focus on the problem of implementing Wald-type tests for nonlinear restrictions. We…

Extending the classical Dirichlet's density theorem on coprime pairs, in this paper we describe completely the probability distribution of the number of coprime pairs in random squares of fixed side length in the lattice $\mathbb{N}^2$. The…

We prove the quenched version of the central limit theorem for the displacement of a random walk in doubly stochastic random environment, under the $H_{-1}$-condition, with slightly stronger, $L^{2+\varepsilon}$ (rather than $L^2$)…

We consider random matrices of the form $H_N=A_N+U_N B_N U^*_N$, where $A_N$, $B_N$ are two $N$ by $N$ deterministic Hermitian matrices and $U_N$ is a Haar distributed random unitary matrix. We establish a universal Central Limit Theorem…

In our previous paper \cite{FTD1}, we derived the almost sure convergence of the global density of eigenvalues of random matrices of the SYK model. In this paper, we will prove the central limit theorem for the linear statistic of…

We introduce and study three new statistics on the hyperoctahedral group $B_{n}$, and show that they give two generalizations of Carlitz's identity for the descent number and major index over $S_{n}$. This answers a question posed by Foata.

We show the relationship between the strongly non-linear limit (also termed the dispersionless or the Whitham limit) of the macroscopic fluctuation theory of certain statistical models and the inverse scattering method. We show that in the…

We study random compositions of transformations having certain uniform fiberwise properties and prove bounds which in combination with other results yield a quenched central limit theorem equipped with a convergence rate, also in the…

We study two types of probability measures on the set of integer partitions of $n$ with at most $m$ parts. The first one chooses the random partition with a chance related to its largest part only. We then obtain the limiting distributions…