Related papers: Moments of random multiplicative functions over fu…
This work computes the asymptotics of the non-integer moments of the logarithmic derivative of characteristic polynomials of matrices from the $SO(2N+1)$ ensemble. It follows from work of Alvarez and Snaith who computed the asymptotics of…
We reconsider the problem of calculating arbitrary negative integer moments of the (regularized) characteristic polynomial for $N\times N$ random matrices taken from the Gaussian Unitary Ensemble (GUE). A very compact and convenient…
We study the moments of the absolute characteristic polynomial of the real elliptic ensemble, including the case of the real Ginibre ensemble. We obtain asymptotics for all integral moments inside the real bulk to order 1 + o(1). In…
We consider parameterized exponential integrals coming from the time evolution of the probability distribution of Brownian motion on globally subanalytic sets. We establish definability results and asymptotic expansions.
Following (Shevtsova, 2010) we introduce detailed classification of the asymptotically exact constants in natural estimates of the rate of convergence in the Lindeberg central limit theorem, namely in Esseen's, Rozovskii's, and Wang-Ahmad's…
We prove Central Limit Theorems and Stein-like bounds for the asymptotic behaviour of nonlinear functionals of spherical Gaussian eigenfunctions. Our investigation combine asymptotic analysis of higher order moments for Legendre polynomials…
We study positive random variables whose moments can be expressed by products and quotients of Gamma functions; this includes many standard distributions. General results are given on existence, series expansion and asymptotics of density…
We give asymptotic expressions for the number of commuting matrices over finite fields. For this, we use product expansions for the corresponding generating functions.
The asymptotic pseudo-trajectory approach to stochastic approximation of Benaim, Hofbauer and Sorin is extended for asynchronous stochastic approximations with a set-valued mean field. The asynchronicity of the process is incorporated into…
In some non-regular statistical estimation problems, the limiting likelihood processes are functionals of fractional Brownian motion (fBm) with Hurst's parameter H; 0 < H <=? 1. In this paper we present several analytical and numerical…
We consider analytic continuations of Fourier transforms and Stieltjes transforms. This enables us to define what we call complex moments for some class of probability measures which do not have moments in the usual sense. There are two…
We prove the two-dimensional analogue of the asymptotics for Toeplitz determinants with Fisher-Hartwig singularities, for general real symbols. This formula has applications to random normal matrices with complex spectra: (i) the…
Moments of the partition rank and crank statistics have been studied for their connections to combinatorial objects such as Durfee symbols, as well as for their connections to harmonic Maass forms. This paper proves a conjecture due to…
We derive exact operator average expressions for the first two spectral moments of nonequilibrium Green's functions for the Falicov-Kimball model and the Hubbard model in the presence of a spatially uniform, time-dependent electric field.…
Statistically self-similar measures on $[0,1]$ are limit of multiplicative cascades of random weights distributed on the $b$-adic subintervals of $[0,1]$. These weights are i.i.d, positive, and of expectation $1/b$. We extend these cascades…
For $a/q\in\mathbb{Q}$ the Estermann function is defined as $D(s,a/q):=\sum_{n\geq1}d(n)n^{-s}\operatorname{e}(n\frac aq)$ if $\Re(s)>1$ and by meromorphic continuation otherwise. For $q$ prime, we compute the moments of $D(s,a/q)$ at the…
We investigate the distribution of monochromatic subgraph counts in random vertex $2$-colorings of large graphs. We give sufficient conditions for the asymptotic normality of these counts and demonstrate their essential necessity…
In various papers the authors have derived asymptotics for moments of certain cotangent sums related to the Riemann Hypothesis. S. Bettin has given an upper bound for the error term in these asymptotic results. In the present paper the…
Self-normalized processes arise naturally in statistical applications. Being unit free, they are not affected by scale changes. Moreover, self-normalization often eliminates or weakens moment assumptions. In this paper we present several…
An asymptotic expansion for inverse moments of positive binomial and Poisson distributions is derived. The expansion coefficients of the asymptotic series are given by the positive central moments of the distribution. Compared to previous…