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Interval-Valued Random Matrices [PDF]
EntropyThis paper introduces a novel approach that combines symbolic data analysis with matrix theory through the concept of interval-valued random matrices.
Abdolnasser Sadeghkhani, Ali Sadeghkhani
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Random matrices and random graphs* [PDF]
ESAIM: Proceedings and Surveys, 2023 We collect recent results on random matrices and random graphs. The topics covered are: fluctuations of the empirical measure of random matrices, finite-size effects of algorithms involving random matrices, characteristic polynomial of sparse matrices ...
Capitaine Mireille +4 more
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On Products of Random Matrices [PDF]
Entropy, 2020 We introduce a family of models, which we name matrix models associated with children’s drawings—the so-called dessin d’enfant. Dessins d’enfant are graphs of a special kind drawn on a closed connected orientable surface (in the sky).
Natalia Amburg +2 more
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Products of Random Matrices [PDF]
Physical Review E, 2002 We derive analytic expressions for infinite products of random 2x2 matrices. The determinant of the target matrix is log-normally distributed, whereas the remainder is a surprisingly complicated function of a parameter characterizing the norm of the ...
A. D. Jackson +6 more
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Growth Quakes and Stasis Using Iterations of Inflating Complex Random Matrices [PDF]
Entropy, 2023 I extend to the case of complex matrices, rather than the case of real matrices as in a prior study, a method of iterating the operation of an “inflating random matrix” onto a state vector to describe complex growing systems. I show that the process also
Henri Benisty
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Black holes and random matrices [PDF]
Journal of High Energy Physics, 2017 We argue that the late time behavior of horizon fluctuations in large anti-de Sitter (AdS) black holes is governed by the random matrix dynamics characteristic of quantum chaotic systems.
Jordan S. Cotler +8 more
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Journal of High Energy Physics, 2023 Black holes are believed to have the fast scrambling properties of random matrices. If the fuzzball proposal is to be a viable model for quantum black holes, it should reproduce this expectation.
Suman Das +3 more
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Introduction to Random Matrices [PDF]
, 1992 These notes provide an introduction to the theory of random matrices. The central quantity studied is $\tau(a)= det(1-K)$ where $K$ is the integral operator with kernel $1/\pi} {\sin\pi(x-y)\over x-y} \chi_I(y)$. Here $I=\bigcup_j(a_{2j-1},a_{2j})$ and $\
A. D. Stone +35 more
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A Spectral Investigation of Criticality and Crossover Effects in Two and Three Dimensions: Short Timescales with Small Systems in Minute Random Matrices [PDF]
EntropyRandom matrix theory, particularly using matrices akin to the Wishart ensemble, has proven successful in elucidating the thermodynamic characteristics of critical behavior in spin systems across varying interaction ranges.
Eliseu Venites Filho +2 more
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Characteristic polynomials of random matrices [PDF]
Communications in Mathematical Physics, 1999 Number theorists have studied extensively the connections between the distribution of zeros of the Riemann $\zeta$-function, and of some generalizations, with the statistics of the eigenvalues of large random matrices.
Brezin, E., Hikami, S.
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