The Jacobi Ensemble*

2020 ◽  
pp. 97-108
Keyword(s):  
Jacobi Ensemble

scholarly journals Jacobi Ensemble, Hurwitz Numbers and Wilson Polynomials

2021 ◽  
Vol 111 (3) ◽  
Author(s):  
Massimo Gisonni ◽  
Tamara Grava ◽  
Giulio Ruzza
Keyword(s):  
Generating Functions ◽  
Combinatorial Interpretation ◽  
Hurwitz Numbers ◽  
Jacobi Ensemble ◽  
Matrix Ensembles ◽  
Wilson Polynomials ◽  
Unitary Ensemble ◽  
Topological Expansion

AbstractWe express the topological expansion of the Jacobi Unitary Ensemble in terms of triple monotone Hurwitz numbers. This completes the combinatorial interpretation of the topological expansion of the classical unitary invariant matrix ensembles. We also provide effective formulæ for generating functions of multipoint correlators of the Jacobi Unitary Ensemble in terms of Wilson polynomials, generalizing the known relations between one point correlators and Wilson polynomials.

GLOBAL FLUCTUATIONS FOR LINEAR STATISTICS OF β-JACOBI ENSEMBLES

2012 ◽  
Vol 01 (04) ◽  
pp. 1250013 ◽  
Author(s):  
IOANA DUMITRIU ◽  
ELLIOT PAQUETTE
Keyword(s):  
Gaussian Process ◽  
Covariance Matrix ◽  
Law Of Large Numbers ◽  
Test Functions ◽  
Linear Statistics ◽  
Jacobi Ensemble ◽  
Large Numbers ◽  
The Mean ◽  
Shifted Chebyshev Polynomial ◽  
Global Fluctuations

We study the global fluctuations for linear statistics of the form [Formula: see text] as n → ∞, for C1 functions f, and λ1, …, λn being the eigenvalues of a (general) β-Jacobi ensemble. The fluctuation from the mean [Formula: see text] turns out to be given asymptotically by a Gaussian process. We compute the covariance matrix for the process and show that it is diagonalized by a shifted Chebyshev polynomial basis; in addition, we analyze the deviation from the predicted mean for polynomial test functions, and we obtain a law of large numbers.

scholarly journals Nonstandard limit theorems and large deviations for the Jacobi beta ensemble

2014 ◽  
Vol 03 (03) ◽  
pp. 1450012 ◽  
Author(s):  
Jan Nagel
Keyword(s):  
Weak Convergence ◽  
Spectral Measure ◽  
Limit Theorems ◽  
Large Deviation ◽  
The Other ◽  
Limit Measure ◽  
Jacobi Ensemble ◽  
Large Deviation Principles ◽  
Beta Ensemble ◽  
Rate Functions

In this paper, we show weak convergence of the empirical eigenvalue distribution and of the weighted spectral measure of the Jacobi ensemble, when one or both parameters grow faster than the dimension n. In these cases, the limit measure is given by the Marchenko–Pastur law and the semicircle law, respectively. For the weighted spectral measure, we also prove large deviation principles under this scaling, where the rate functions are those of the other classical ensembles.

scholarly journals Rectangular Young tableaux and the Jacobi ensemble

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Philippe Marchal
Keyword(s):  
Young Tableaux ◽  
Random Surface ◽  
Jacobi Ensemble ◽  
International Audience ◽  
Deterministic Limit

International audience It has been shown by Pittel and Romik that the random surface associated with a large rectangular Youngtableau converges to a deterministic limit. We study the fluctuations from this limit along the edges of the rectangle.We show that in the corner, these fluctuations are gaussian whereas, away from the corner and when the rectangle isa square, the fluctuations are given by the Tracy-Widom distribution. Our method is based on a connection with theJacobi ensemble.

A matrix model for the β-Jacobi ensemble

2003 ◽  
Vol 44 (10) ◽  
pp. 4807 ◽  
Author(s):  
Ross A. Lippert
Keyword(s):  
Matrix Model ◽  
Jacobi Ensemble
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