English
Related papers

Related papers: Disk counting statistics near hard edges of random…

200 papers

We study the derivative of the characteristic polynomial of $N \times N$ Haar distributed unitary matrices. We obtain the first explicit formulae for complex-valued moments when the spectral variable is inside the unit disc, in the limit $N…

Probability · Mathematics 2024-12-24 Nick Simm , Fei Wei

The large $N$ asymptotic expansion of the partition function for the normal matrix model is predicted to have special features inherited from its interpretation as a two-dimensional Coulomb gas. However for the latter, it is most natural to…

Probability · Mathematics 2025-06-18 Matthias Allard , Peter J. Forrester , Sampad Lahiry , Bojian Shen

We analytically compute the full counting statistics of charge transfer in a classical automaton of interacting charged particles. Deriving a closed-form expression for the moment generating function with respect to a stationary equilibrium…

Statistical Mechanics · Physics 2024-02-06 Žiga Krajnik , Johannes Schmidt , Vincent Pasquier , Enej Ilievski , Tomaž Prosen

We formulate the statistics of the discrete multicomponent fragmentation event using a methodology borrowed from statistical mechanics. We generate the ensemble of all feasible distributions that can be formed when a single integer…

Statistical Mechanics · Physics 2020-07-03 Themis Matsoukas

Given an integer m>=1, let || || be a norm in R^{m+1} and let S denote the set of points with nonnegative coordinates in the unit sphere with respect to this norm. Consider for each 1<= j<= m a function f_j(z) that is analytic in an open…

Combinatorics · Mathematics 2007-06-13 Manuel Lladser

We use a semi-Markov process method to calculate large deviations of counting statistics for three open quantum systems, including a resonant two-level system and resonant three-level systems in the $\Lambda$- and $V$-configurations. In the…

Statistical Mechanics · Physics 2023-12-15 Fei Liu

This is the first of a series of three articles that treats fracture localization as a critical phenomenon. This first article establishes a statistical mechanics based on ensemble averages when fluctuations through time play no role in…

Statistical Mechanics · Physics 2009-11-07 Renaud Toussaint , Steven R. Pride

We create collectively jammed (CJ) packings of 50-50 bidisperse mixtures of smooth disks in 2d using an algorithm in which we successively compress or expand soft particles and minimize the total energy at each step until the particles are…

Statistical Mechanics · Physics 2009-11-11 Ning Xu , Jerzy Blawzdziewicz , Corey S. O'Hern

We study the partition function from random matrix theory using a well known connection to orthogonal polynomials, and a recently developed Riemann-Hilbert approach to the computation of detailed asymptotics for these orthogonal…

Mathematical Physics · Physics 2007-05-23 N. M. Ercolani , K. D. T-R McLaughlin

We consider two-dimensional determinantal processes which are rotation-invariant and study the fluctuations of the number of points in disks. Based on the theory of mod-phi convergence, we obtain Berry-Esseen as well as precise moderate to…

Probability · Mathematics 2020-05-28 Marcel Fenzl , Gaultier Lambert

We study the behavior of configurations in the symmetric six-vertex model with $a,b,c$ weights in the $n\times n$ square with Domain Wall Boundary Conditions as $n\to\infty$. We prove that when $\Delta=\frac{a^2+b^2-c^2}{2ab}<1$,…

Probability · Mathematics 2023-10-20 Vadim Gorin , Karl Liechty

We investigate the limiting behavior of discrete determinantal point processes (DPPs) towards continuous DPPs when the size of the set to sample from goes to infinity. We propose a non-asymptotic characterization of this limit in terms of…

Probability · Mathematics 2026-03-03 Hugo Jaquard , Nicolas Keriven

We introduce a two parameter ($\alpha, \beta>-1$) family of interacting particle systems with determinantal correlation kernels expressible in terms of Jacobi polynomials $\{ P^{(\alpha, \beta)}_k \}_{k \geq 0}$. The family includes…

Probability · Mathematics 2017-08-08 Mark Cerenzia , Jeffrey Kuan

In this paper, we analyze the asymptotic behavior of the main characteristics of the mean-variance efficient frontier employing random matrix theory. Our particular interest covers the case when the dimension $p$ and the sample size $n$…

Statistical Finance · Quantitative Finance 2024-09-24 Taras Bodnar , Nikolaus Hautsch , Yarema Okhrin , Nestor Parolya

We conclude our work [arXiv:2403.07628, arXiv:2503.12644] on asymptotic expansions at the soft edge for the classical $n$-dimensional Gaussian and Laguerre ensembles, now studying the gap-probability generating functions. We show that the…

Probability · Mathematics 2026-05-18 Folkmar Bornemann

Discrete random probability measures are a key ingredient of Bayesian nonparametric inferential procedures. A sample generates ties with positive probability and a fundamental object of both theoretical and applied interest is the…

Statistics Theory · Mathematics 2021-01-20 Pierpaolo De Blasi , Ramsés H. Mena , Igor Prünster

A joint limit theorem for the point process of the off-diagonal entries of a sample covariance matrix $\mathbf{S}$, constructed from $n$ observations of a $p$-dimensional random vector with iid components, and the Frobenius norm of…

Probability · Mathematics 2023-02-28 Johannes Heiny , Carolin Kleemann

We present the algorithmic procedure determining the impulsive behavior of a rigid disk having a single or possibly multiple frictionless impact with two walls forming a corner. The algorithmic procedure represents an application of the…

Numerical Analysis · Mathematics 2019-02-15 Claudia Fassino , Stefano Pasquero

We propose a new method for obtaining complete asymptotic expansions in a systematic manner, which is suitable for counting sequences of various graph families in dense regime. The core idea is to encode the two-dimensional array of…

Combinatorics · Mathematics 2024-12-02 Sergey Dovgal , Khaydar Nurligareev

We consider a multivariate generating function F(z), whose coefficients are indexed by d-tuples of nonnegative integers: F(z) = sum_r a_r z^r where z^r denotes the product of z_j^{r_j} over j = 1, ..., d. Suppose that F(z) is meromorphic in…

Combinatorics · Mathematics 2007-05-23 Robin Pemantle , Mark Wilson