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.

Level Spacing Distributions of Random Matrix Ensembles

1993 ◽  
Vol 62 (7) ◽  
pp. 2248-2259 ◽  
Author(s):  
Masahiro Shiroishi ◽  
Taro Nagao ◽  
Miki Wadati
Keyword(s):  
Random Matrix ◽  
Level Spacing ◽  
Random Matrix Ensembles ◽  
Matrix Ensembles

scholarly journals Gaussian perturbations of hard edge random matrix ensembles

Nonlinearity ◽  
2016 ◽  
Vol 29 (11) ◽  
pp. 3385-3416 ◽  
Author(s):  
Tom Claeys ◽  
Antoine Doeraene
Keyword(s):  
Random Matrix ◽  
Hard Edge ◽  
Random Matrix Ensembles ◽  
Matrix Ensembles

scholarly journals Modelling equilibration of local many-body quantum systems by random graph ensembles

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 273 ◽  
Author(s):  
Daniel Nickelsen ◽  
Michael Kastner
Keyword(s):  
Hilbert Space ◽  
Random Matrices ◽  
Network Theory ◽  
Maximum Flow ◽  
Quantum Systems ◽  
Complex Matrix ◽  
Many Body ◽  
Random Matrix Ensembles ◽  
Matrix Ensembles ◽  
Exact Diagonalisation

We introduce structured random matrix ensembles, constructed to model many-body quantum systems with local interactions. These ensembles are employed to study equilibration of isolated many-body quantum systems, showing that rather complex matrix structures, well beyond Wigner's full or banded random matrices, are required to faithfully model equilibration times. Viewing the random matrices as connectivities of graphs, we analyse the resulting network of classical oscillators in Hilbert space with tools from network theory. One of these tools, called the maximum flow value, is found to be an excellent proxy for equilibration times. Since maximum flow values are less expensive to compute, they give access to approximate equilibration times for system sizes beyond those accessible by exact diagonalisation.

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