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Maximum entropy models, motivated by applications in neuron science, are natural generalizations of the $\beta$-model to weighted graphs. Similar to the $\beta$-model, each vertex in maximum entropy models is assigned a potential parameter,…

Statistics Theory · Mathematics 2014-10-28 Ting Yan , Yunpeng Zhao , Hong Qin

Inter-relations between random matrix ensembles with different symmetry types provide inter-relations between generating functions for the gap probabilites at the spectrum edge. Combining these in the scaled limit with the exact evaluation…

Mathematical Physics · Physics 2007-05-23 P. J. Forrester

The $\beta$ ensembles are a class of eigenvalue probability densities which generalise the invariant ensembles of classical random matrix theory. In the case of the Gaussian and Laguerre weights, the corresponding eigenvalue densities are…

Mathematical Physics · Physics 2018-12-20 Peter J. Forrester , Allan K. Trinh

Asymptotic expansions are presented for the moments of bound states in one-dimensional anharmonic potentials. The results are derived by using the SAFE method and include only the first non-zero wave-related correction to the familiar…

Quantum Physics · Physics 2023-05-31 G. W. Forbes , Miguel A. Alonso

The aim of this paper is to use non asymptotic bounds for the probability of rare events in the Sanov theorem, in order to study the asymptotics in conditional limit theorems (Gibbs conditioning principle for thin sets). Applications to…

Probability · Mathematics 2007-05-23 Patrick Cattiaux , Nathael Gozlan

In this article we review recent generalisations of the central limit theorem for the sum of specially correlated (or q-independent) variables, focusing on q greater or equal than 1. Specifically, this kind of correlation turns the…

Statistical Mechanics · Physics 2007-12-16 Silvio M. Duarte Queiros , Constantino Tsallis

In the edge-2star model with hard constraints we prove the existence of an open set of constraint parameters, bisected by a line segment on which there are nonunique entropy-optimal graphons related by a symmetry. At each point in the open…

Probability · Mathematics 2026-01-26 Charles Radin , Lorenzo Sadun

Asymptotics of maximum likelihood estimation for $\alpha$-stable law are analytically investigated with a continuous parameterization. The consistency and asymptotic normality are shown on the interior of the whole parameter space. Although…

Statistics Theory · Mathematics 2019-03-01 Muneya Matsui

We consider a $\mathbb{R}$-extension of one dimensional uniformly expanding open dynamical systems and prove a new explicit estimate for the asymptotic spectral gap. To get these results, we use a new application of a "global normal form"…

Dynamical Systems · Mathematics 2017-08-11 Frédéric Faure , Tobias Weich

Weak convergence of the empirical copula process is shown to hold under the assumption that the first-order partial derivatives of the copula exist and are continuous on certain subsets of the unit hypercube. The assumption is…

Statistics Theory · Mathematics 2012-07-06 Johan Segers

We analyze the asymptotic number and typical structure of claw-free graphs at constant edge densities. The first of our main results is a formula for the asymptotics of the logarithm of the number of claw-free graphs of edge density $\gamma…

Combinatorics · Mathematics 2025-01-30 Will Perkins , Sam van der Poel

It is well known that the edge limit of Gaussian/Laguerre Beta-ensembles, as well as a large class of $\beta$-ensembles is given by the $\mathrm{Airy}(\beta)$ point process. We extend this universality result to a general class of additions…

Probability · Mathematics 2026-03-16 David Keating , Jiaming Xu

We develop a quenched thermodynamic formalism for open random dynamical systems generated by finitely branched, piecewise-monotone mappings of the interval. The openness refers to the presence of holes in the interval, which terminate…

Dynamical Systems · Mathematics 2021-03-09 Jason Atnip , Gary Froyland , Cecilia González-Tokman , Sandro Vaienti

Probabilistic omega-automata are variants of nondeterministic automata for infinite words where all choices are resolved by probabilistic distributions. Acceptance of an infinite input word can be defined in different ways: by requiring…

Formal Languages and Automata Theory · Computer Science 2009-07-29 Christel Baier , Nathalie Bertrand , Marcus Größer

Variable-length compression without prefix-free constraints and with side-information available at both encoder and decoder is considered. Instead of requiring the code to be error-free, we allow for it to have a non-vanishing error…

Information Theory · Computer Science 2020-08-24 Yuta Sakai , Vincent Y. F. Tan

This article is focused on the asymptotic expansions, as time tends to infinity, of solutions of a system of ordinary differential equations with non-smooth nonlinear terms. The forcing function decays to zero in a very complicated but…

Classical Analysis and ODEs · Mathematics 2024-11-04 Luan Hoang

The maximum likelihood estimator (MLE) is pivotal in statistical inference, yet its application is often hindered by the absence of closed-form solutions for many models. This poses challenges in real-time computation scenarios,…

Methodology · Statistics 2025-04-16 Pedro L. Ramos , Eduardo Ramos , Francisco A. Rodrigues , Francisco Louzada

We give a streamlined proof of a quantitative version of a result from [DG1] which is crucial for the proof of universality in the bulk [DG1] and also at the edge [DG2] for orthogonal and symplectic ensembles of random matrices. As a…

Mathematical Physics · Physics 2007-05-23 Ovidiu Costin , Percy Deift , Dimitri Gioev

A consistent generalization of statistical mechanics is obtained by applying the maximum entropy principle to a trace-form entropy and by requiring that physically motivated mathematical properties are preserved. The emerging…

Statistical Mechanics · Physics 2009-11-10 G. Kaniadakis , M. Lissia , A. M. Scarfone

In Bayesian nonparametric inference, random discrete probability measures are commonly used as priors within hierarchical mixture models for density estimation and for inference on the clustering of the data. Recently, it has been shown…

Statistics Theory · Mathematics 2012-11-26 Stefano Favaro , Antonio Lijoi , Igor Prünster