Random-matrix theories in quantum physics: common concepts
T Guhr, A Müller–Groeling, HA Weidenmüller - Physics Reports, 1998 - Elsevier
We review the development of random-matrix theory (RMT) during the last fifteen years. We
emphasize both the theoretical aspects, and the application of the theory to a number of …
emphasize both the theoretical aspects, and the application of the theory to a number of …
JT gravity and the ensembles of random matrix theory
D Stanford, E Witten - arXiv preprint arXiv:1907.03363, 2019 - arxiv.org
We generalize the recently discovered relationship between JT gravity and double-scaled
random matrix theory to the case that the boundary theory may have time-reversal symmetry …
random matrix theory to the case that the boundary theory may have time-reversal symmetry …
Nonperturbative Jackiw-Teitelboim gravity
CV Johnson - Physical Review D, 2020 - APS
Recently, Saad et al. showed how to define the genus expansion of Jackiw-Teitelboim (JT)
quantum gravity in terms of a double-scaled Hermitian matrix model. However, the model's …
quantum gravity in terms of a double-scaled Hermitian matrix model. However, the model's …
Non-hermitian random matrix theory: Method of hermitian reduction
J Feinberg, A Zee - Nuclear Physics B, 1997 - Elsevier
We consider random non-hermitian matrices in the large-N limit. The power of analytic
function theory cannot be brought to bear directly to analyze non-hermitian random matrices …
function theory cannot be brought to bear directly to analyze non-hermitian random matrices …
Biorthogonal ensembles
A Borodin - Nuclear Physics B, 1998 - Elsevier
One object of interest in random matrix theory is a family of point ensembles (ramdom point
configurations) related to various systems of classical orthogonal polynomials. The paper …
configurations) related to various systems of classical orthogonal polynomials. The paper …
How instanton combinatorics solves Painlevé VI, V and IIIs
We elaborate on a recently conjectured relation of Painlevé transcendents and 2D
conformal field theory. General solutions of Painlevé VI, V and III are expressed in terms of …
conformal field theory. General solutions of Painlevé VI, V and III are expressed in terms of …
Quantum mechanical time-delay matrix in chaotic scattering
We calculate the probability distribution of the matrix Q=− i ħ S− 1∂ S/∂ E for a chaotic
system with scattering matrix S at energy E. The eigenvalues τ j of Q are the so-called proper …
system with scattering matrix S at energy E. The eigenvalues τ j of Q are the so-called proper …
Topological phases and delocalization of quantum walks in random environments
H Obuse, N Kawakami - Physical Review B—Condensed Matter and Materials …, 2011 - APS
We investigate one-dimensional (1D) discrete-time quantum walks (QWs) with spatially or
temporally random defects as a consequence of interactions with random environments. We …
temporally random defects as a consequence of interactions with random environments. We …
Complete random matrix classification of SYK models with = 0, 1 and 2 supersymmetry
T Kanazawa, T Wettig - Journal of High Energy Physics, 2017 - Springer
A bstract We present a complete symmetry classification of the Sachdev-Ye-Kitaev (SYK)
model with\(\mathcal {N}\)= 0, 1 and 2 supersymmetry (SUSY) on the basis of the Altland …
model with\(\mathcal {N}\)= 0, 1 and 2 supersymmetry (SUSY) on the basis of the Altland …
The microstate physics of JT gravity and supergravity
CV Johnson - arXiv preprint arXiv:2201.11942, 2022 - arxiv.org
It is proposed that a complete understanding of two-dimensional quantum gravity and its
emergence in random matrix models requires fully embracing {\it both} Wigner (statistics) …
emergence in random matrix models requires fully embracing {\it both} Wigner (statistics) …