A probabilistic computation of a Mehta integral
Probability
2024-08-13 v1
Authors:
Liviu I. Nicolaescu
Abstract
We use the Kac-Rice formula to compute the Mehta integral describing the normalization constant arising in the statistics of the Gaussian Orthogonal Ensemble.
Cite
@article{arxiv.2408.06203,
title = {A probabilistic computation of a Mehta integral},
author = {Liviu I. Nicolaescu},
journal= {arXiv preprint arXiv:2408.06203},
year = {2024}
}
Comments
10 pages
Related papers
View all related →
Disordered Systems and Neural Networks · Physics
Generalized Lotka-Volterra equations with random, non-reciprocal interactions: the typical number of equilibria
Valentina Ros, Felix Roy, Giulio Biroli, Guy Bunin +1
2023-06-27
Disordered Systems and Neural Networks · Physics
Quenched complexity of equilibria for asymmetric Generalized Lotka-Volterra equations
Valentina Ros, Felix Roy, Giulio Biroli, Guy Bunin
2023-06-27
Computation · Statistics
Computation of Gaussian orthant probabilities in high dimension
James Ridgway
2014-11-26
Number Theory · Mathematics
Mean Values of the Logarithmic Derivative of the zeta Function and the GUE Hypothesis
David W. Farmer
2009-09-25
Probability · Mathematics
A novel computational framework for the expected number of real roots of stochastic functions on a given interval
Xu Yi
2026-03-03
Statistics Theory · Mathematics
On the number of modes of Gaussian kernel density estimators
Borjan Geshkovski, Philippe Rigollet, Yihang Sun
2025-11-10
Probability · Mathematics
Kac-Rice formula for transverse intersections
Michele Stecconi
2021-03-22
Disordered Systems and Neural Networks · Physics
Complex energy landscapes in spiked-tensor and simple glassy models: ruggedness, arrangements of local minima and phase transitions
Valentina Ros, Gerard Ben Arous, Giulio Biroli, Chiara Cammarota
2019-01-09
Probability · Mathematics
Critical Points of Chi-Fields
Domenico Marinucci, Michele Stecconi
2024-10-01
Mathematical Physics · Physics
On the superintegrability of the Gaussian $\beta$ ensemble and its $(q,t)$ generalisation
Sung-Soo Byun, Peter J. Forrester
2025-05-20
Probability · Mathematics
Gaussian fluctuations of eigenvalues in the GUE
Jonas Gustavsson
2015-06-26
Probability · Mathematics
Two-dimensional Kac-Rice formula. Application to shot noise processes excursions
Raphaël Lachièze-Rey
2016-07-20
Statistical Mechanics · Physics
The Index Distribution of Gaussian Random Matrices
Satya N. Majumdar, Celine Nadal, Antonello Scardicchio, Pierpaolo Vivo
2015-05-14
Statistics Theory · Mathematics
Bayesian inference and prediction for mean-mixtures of normal distributions
Pankaj Bhagwat, Eric Marchand
2022-02-02
Numerical Analysis · Mathematics
Kac-Rice formulas and the number of solutions of parametrized systems of polynomial equations
Elisenda Feliu, AmirHosein Sadeghimanesh
2022-05-18
Statistics Theory · Mathematics
Expectations of some ratio-type estimators under the gamma distribution
Jia-Han Shih
2025-05-09
Methodology · Statistics
Estimating orthant probabilities of high dimensional Gaussian vectors with an application to set estimation
Dario Azzimonti, David Ginsbourger
2018-12-03
Statistical Mechanics · Physics
The Calogero-Moser equation system and the ensemble average in the Gaussian ensembles
H. -J. Stoeckmann
2009-11-10
Probability · Mathematics
Generalized $\beta$-Gaussian Ensemble Equilibrium measure method
Mohamed Bouali
2014-09-02
Statistical Mechanics · Physics
Fluctuation formula for complex random matrices
P. J. Forrester
2007-05-23
Classical Analysis and ODEs · Mathematics
Kac-Rice formula: A contemporary overview of the main results and applications
Corinne Berzin, Alain Latour, José León
2022-05-19
Machine Learning · Statistics
On the Wasserstein Geodesic Principal Component Analysis of probability measures
Nina Vesseron, Elsa Cazelles, Alice Le Brigant, Thierry Klein
2025-06-06
Data Structures and Algorithms · Computer Science
A Cubic Algorithm for Computing Gaussian Volume
Ben Cousins, Santosh Vempala
2013-07-12
Representation Theory · Mathematics
The stable wave front set of theta representations
Edmund Karasiewicz, Emile Okada, Runze Wang
2024-11-05
Probability · Mathematics
Gaussian Fluctuations of Eigenvalues in Wigner Random Matrices
Sean O'Rourke
2011-03-03