English
Related papers

Related papers: Moments of random multiplicative functions over fu…

200 papers

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…

Mathematical Physics · Physics 2023-03-15 Emilia Alvarez , Pierre Bousseyroux , Nina C. Snaith

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…

Mathematical Physics · Physics 2009-11-07 Yan V Fyodorov

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…

Probability · Mathematics 2024-10-11 Pax Kivimae

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.

Classical Analysis and ODEs · Mathematics 2017-10-20 Tobias Kaiser , Julia Ruppert

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…

Probability · Mathematics 2021-01-13 Ruslan Gabdullin , Vladimir Makarenko , Irina Shevtsova

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…

Mathematical Physics · Physics 2015-06-11 Domenico Marinucci , Igor Wigman

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…

Probability · Mathematics 2010-02-23 Svante Janson

We give asymptotic expressions for the number of commuting matrices over finite fields. For this, we use product expansions for the corresponding generating functions.

Number Theory · Mathematics 2026-02-20 Kathrin Bringmann , Shane Chern , Johann Franke , Bernhard Heim

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…

Machine Learning · Statistics 2011-12-13 Steven Perkins , David S. Leslie

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…

Statistics Theory · Mathematics 2014-06-06 Alexander Novikov , Nino Kordzakhia , Timothy Ling

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…

Probability · Mathematics 2013-12-04 Takahiro Hasebe

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…

Probability · Mathematics 2026-01-13 Paul Bourgade , Guillaume Dubach , Lisa Hartung , Ahmet Keles

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…

Number Theory · Mathematics 2014-02-26 K. Bringmann , K. Mahlburg , R. Rhoades

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.…

Strongly Correlated Electrons · Physics 2009-11-11 V. M. Turkowski , J. K. Freericks

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…

Probability · Mathematics 2009-02-18 Julien Barral , Benoit Mandelbrot

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…

Number Theory · Mathematics 2019-03-27 Sandro Bettin

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…

Probability · Mathematics 2024-03-22 Nitya Mani , Dan Mikulincer

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…

Classical Analysis and ODEs · Mathematics 2018-06-05 Helmut Maier , Michael Th. Rassias

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…

Probability · Mathematics 2007-05-23 Victor H. de la Pena , Michael J. Klass , Tze Leung Lai

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…

Statistics Theory · Mathematics 2009-01-16 Marko Znidaric