scholarly journals Muttalib–Borodin ensembles in random matrix theory — realisations and correlation functions

2017 ◽  
Vol 22 (0) ◽  
Author(s):  
Peter J. Forrester ◽  
Dong Wang
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Correlation Functions ◽  
Matrix Theory

scholarly journals UNIVERSAL CORRELATIONS IN RANDOM MATRICES: QUANTUM CHAOS, THE 1/r2 INTEGRABLE MODEL, AND QUANTUM GRAVITY

1996 ◽  
Vol 11 (15) ◽  
pp. 1201-1219 ◽  
Author(s):  
SANJAY JAIN
Keyword(s):  
Quantum Gravity ◽  
Random Matrices ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Correlation Functions ◽  
Quantum Chaos ◽  
Matrix Theory ◽  
Mathematical Formulation ◽  
Integrable Model ◽  
Moser System

Random matrix theory (RMT) provides a common mathematical formulation of distinct physical questions in three different areas: quantum chaos, the 1-D integrable model with the 1/r2 interaction (the Calogero-Sutherland-Moser system) and 2-D quantum gravity. We review the connection of RMT with these areas. We also discuss the method of loop equations for determining correlation functions in RMT, and smoothed global eigenvalue correlators in the two-matrix model for Gaussian orthogonal, unitary and symplectic ensembles.

scholarly journals Spectral decoupling in many-body quantum chaos

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Jordan Cotler ◽  
Nicholas Hunter-Jones
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Correlation Functions ◽  
Quantum Chaos ◽  
Matrix Theory ◽  
Energy Eigenvalue ◽  
Time Dependent ◽  
Late Time ◽  
Many Body ◽  
Many Body Systems

Abstract We argue that in a large class of disordered quantum many-body systems, the late time dynamics of time-dependent correlation functions is captured by random matrix theory, specifically the energy eigenvalue statistics of the corresponding ensemble of disordered Hamiltonians. We find that late time correlation functions approximately factorize into a time-dependent piece, which only depends on spectral statistics of the Hamiltonian ensemble, and a time-independent piece, which only depends on the data of the constituent operators of the correlation function. We call this phenomenon “spectral decoupling”, which signifies a dynamical onset of random matrix theory in correlation functions. A key diagnostic of spectral decoupling is k-invariance, which we refine and study in detail. Particular emphasis is placed on the role of symmetries, and connections between k-invariance, scrambling, and OTOCs. Disordered Pauli spin systems, as well as the SYK model and its variants, provide a rich source of disordered quantum many-body systems with varied symmetries, and we study k-invariance in these models with a combination of analytics and numerics.

SSA, Random Matrix Theory, and Noise-Reduced Correlations

2016 ◽  
Author(s):  
Jan W Dash ◽  
Xipei Yang ◽  
Mario Bondioli ◽  
Harvey J. Stein
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory

History—an overview

2018 ◽  
Author(s):  
Oriol Bohigas ◽  
Hans A. Weidenmüller
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Rapid Development ◽  
The Past ◽  
History Of ◽  
And Mathematics

An overview of the history of random matrix theory (RMT) is provided in this chapter. Starting from its inception, the authors sketch the history of RMT until about 1990, focusing their attention on the first four decades of RMT. Later developments are partially covered. In the past 20 years RMT has experienced rapid development and has expanded into a number of areas of physics and mathematics.

scholarly journals Extremal correlators and random matrix theory

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Alba Grassi ◽  
Zohar Komargodski ◽  
Luigi Tizzano
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Matrix Model ◽  
Effective Field Theory ◽  
Random Matrix ◽  
Correlation Functions ◽  
Matrix Theory ◽  
Effective Field ◽  
Random Matrix Model ◽  
Large Charge

Abstract We study the correlation functions of Coulomb branch operators of four-dimensional $$ \mathcal{N} $$ N = 2 Superconformal Field Theories (SCFTs). We focus on rank-one theories, such as the SU(2) gauge theory with four fundamental hypermultiplets. “Extremal” correlation functions, involving exactly one anti-chiral operator, are perhaps the simplest nontrivial correlation functions in four-dimensional Quantum Field Theory. We show that the large charge limit of extremal correlators is captured by a “dual” description which is a chiral random matrix model of the Wishart-Laguerre type. This gives an analytic handle on the physics in some particular excited states. In the limit of large random matrices we find the physics of a non-relativistic axion-dilaton effective theory. The random matrix model also admits a ’t Hooft expansion in which the matrix is taken to be large and simultaneously the coupling is taken to zero. This explains why the extremal correlators of SU(2) gauge theory obey a nontrivial double scaling limit in states of large charge. We give an exact solution for the first two orders in the ’t Hooft expansion of the random matrix model and compare with expectations from effective field theory, previous weak coupling results, and we analyze the non-perturbative terms in the strong ’t Hooft coupling limit. Finally, we apply the random matrix theory techniques to study extremal correlators in rank-1 Argyres-Douglas theories. We compare our results with effective field theory and with some available numerical bootstrap bounds.

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