Related papers: Sectorial convergence of U-statistics

In this work we prove an asymptotic result, that under some conditions on the involved distribution functions, is valid for any Oppenheim expansion, extending a classical result proven by W. Vervaat in 1972 for denominators of the Luroth…

The theory of convergent graph sequences has been worked out in two extreme cases, dense graphs and bounded degree graphs. One can define convergence in terms of counting homomorphisms from fixed graphs into members of the sequence…

In this article, we provide a unified framework for studying the convergence of rescaled characteristic polynomials of random matrices from various classical ensembles as well as functional convergence results for the Riemann zeta function.…

We study the convergence of centered and normalized sums of i.i.d. random elements of the space $\mathcal{D}$ of c{{\'a}}dl{{\'a}}g functions endowed with Skorohod's $J\_1$ topology, to stable distributions in $\mathcal D$. Our results are…

We study the behavior of the Riemann zeta function on the critical line when the imaginary part of the argument is sampled by the Cauchy random walk. We develop a complete second order theory for the corresponding system of random variables…

The purpose of this paper is to establish the almost sure weak ergodic convergence of a sequence of iterates $(x_n)$ given by $x_{n+1} = (I+\lambda_n A(\xi_{n+1},\,.\,))^{-1}(x_n)$ where $(A(s,\,.\,):s\in E)$ is a collection of maximal…

The Conley-Zehnder index associates an integer to any continuous path of symplectic matrices starting from the identity and ending at a matrix which does not admit 1 as an eigenvalue. We give new ways to compute this index. Robbin and…

Let $U\in U(N)$ be a random unitary matrix of size $N$, distributed with respect to the Haar measure on $U(N)$. Let $P(z)=P_U(z)$ be the characteristic polynomial of $U$. We prove that for $z$ close to the unit circle, $ \frac{P'}{P}(z) $…

In this note, we give sufficient conditions for the almost sure and the convergence in $\mathbb{L}^p$ of a $U$-statistic of order $m$ built on a strictly stationary but not necessarily ergodic sequence.

In this paper we introduce the notions of statistical convergence and statistical Cauchyness of sequences in a metric-like space. We study some basic properties of these notions

Let $S_r(p,q)$ be the $r$-associated Stirling numbers of the second kind, the number of ways to partition a set of size $p$ into $q$ subsets of size at least $r$. For $r=1$, these are the standard Stirling numbers of the second kind, and…

We prove that the asymptotic of the bulk local statistics in models of random lozenge tilings is universal in the vicinity of straight boundaries of the tiled domains. The result applies to uniformly random lozenge tilings of large…

In this note, we establish the convergence in distribution of the maxima of i.i.d. random variables to the Gumbel distribution with the associated normalizing sequences for several examples that are related to the normal distribution.…

In 1970, based on newly available empiric evidence, a remarkable monotonicity property for $| \zeta(z) |$ was conjectured by R. Spira. The $\zeta$-monotonicity property can be written as follows: $$ | \zeta (x_2 + y i ) | < | \zeta \left (…

We prove that any non-zero complex values $z_1,\ldots,z_n$ can be approximated by the following integral shifts of the Riemann zeta-function $\zeta(s+id_1\tau),\ldots,\zeta(s+id_n\tau)$ for infinitely many $\tau$, provided…

Recent proofs of the convergence of the linear delta expansion in zero and in one dimensions have been limited to the analogue of the vacuum generating functional in field theory. In zero dimensions it was shown that with an appropriate,…

In this paper, we prove analogues of Khintchine and Rosenthal's moment inequalities for symmetric statistics (U-statistics) of arbitrary order. An example that shows significance of each term in the analogues of Rosenthal's bounds for…

Linear statistics of random zero sets are integrals of smooth differential forms over the zero set and as such are smooth analogues of the volume of the random zero set inside a fixed domain. We derive an asymptotic expansion for the…

We study the density of the roots of the derivative of the characteristic polynomial Z(U,z) of an N x N random unitary matrix with distribution given by Haar measure on the unitary group. Based on previous random matrix theory models of the…

Let $Z_1,\, Z_2,\dots$ be independent and identically distributed complex random variables with common distribution $\mu$ and set $$ P_n(z) := (z - Z_1)\cdots (z - Z_n)\,. $$ Recently, Angst, Malicet and Poly proved that the critical points…