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Crystallization of random matrix orbits [PDF]

International Mathematics Research Notices, 2018
Three operations on eigenvalues of real/complex/quaternion (corresponding to $\beta=1,2,4$) matrices, obtained from cutting out principal corners, adding, and multiplying matrices can be extrapolated to general values of $\beta>0$ through associated ...
Gorin, Vadim, Marcus, Adam W.
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Random Matrix Transformation and Its Application in Image Hiding [PDF]

Sensors, 2023
Image coding technology has become an indispensable technology in the field of modern information. With the vigorous development of the big data era, information security has received more attention.
Jijun Wang, Fun Soo Tan, Yi Yuan
doaj   +2 more sources

Glassy Random Matrix Models [PDF]

Physical Review E, 2002
This paper discusses Random Matrix Models which exhibit the unusual phenomena of having multiple solutions at the same point in phase space. These matrix models have gaps in their spectrum or density of eigenvalues.
A. Kamenev, C-I Tan, C-I Tan, C. Crnkkovic, C. Nappi, D. Bessis, D. Bessis, D. Gross, D. Senechal, E. Brézin, E. Brézin, E. Kanzieper, E. Marinari, G. Akemann, G. Akemann, G. Akemann, G. Bhanot, G. Bonnet, G.M. Cicuta, G.M. Cicuta, H. Neuberger, J. Ambjorn, J. Distler, J. Harer, J. Jurkiewicz, K. Demeterfi, L.F. Cugliandolo, M. Bowick, M. Douglas, M. Sasaki, N. Deo, N. Deo, O. Lechtenfeld, O. Lechtenfeld, P. Deift, P. Deift, P. Mathieu, P.M.S. Petropoulos, R.C. Brower, R.C. Penner, R.C. Penner, S. Dalley, T. Guhr, T. Hollowood, V.A. Kazakov, Y. Shimamune   +45 more
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Integrable random matrix ensembles [PDF]

Nonlinearity, 2011
We propose new classes of random matrix ensembles whose statistical properties are intermediate between statistics of Wigner-Dyson random matrices and Poisson statistics.
Bogomolny, E., Giraud, O., Schmit, C.
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Developments in Random Matrix Theory [PDF]

Journal of Physics A: Mathematical and General, 2003
In this preface to the Journal of Physics A, Special Edition on Random Matrix Theory, we give a review of the main historical developments of random matrix theory.
Forrester, P. J., Snaith, N. C., Verbaarschot, J. J. M.   +2 more
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Autocorrelation of Random Matrix Polynomials [PDF]

Communications in Mathematical Physics, 2003
We calculate the autocorrelation functions (or shifted moments) of the characteristic polynomials of matrices drawn uniformly with respect to Haar measure from the groups U(N), O(2N) and USp(2N).
Conrey, J. B., Farmer, D. W., Keating, J. P., Rubinstein, M. O., Snaith, N. C.   +4 more
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Quasiclassical Random Matrix Theory [PDF]

Physical Review Letters, 1996
We directly combine ideas of the quasiclassical approximation with random matrix theory and apply them to the study of the spectrum, in particular to the two-level correlator.
A. L. Andreev, A. V. Andreev, A. Voros, B. Dietz, B. Georgeot, E. B. Bogomolny, E. B. Bogomolny, E. Doron, G. Szegö, H. U. Baranger, J. H. Hannay, K. A. Muttalib, M. C. Gutzwiller, M. C. Gutzwiller, M. L. Mehta, M. V. Berry, M. V. Berry, M. V. Berry, N. Argaman, O. Agam, O. Agam, R. Balian, R. Balian, R. E. Prange   +23 more
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Optimized Tail Bounds for Random Matrix Series [PDF]

Entropy
Random matrix series are a significant component of random matrix theory, offering rich theoretical content and broad application prospects. In this paper, we propose modified versions of tail bounds for random matrix series, including matrix Gaussian ...
Xianjie Gao, Mingliang Zhang, Jinming Luo   +2 more
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A random matrix approach to decoherence [PDF]

Journal of Optics B: Quantum and Semiclassical Optics, 2001
In order to analyze the effect of chaos or order on the rate of decoherence in a subsystem, we aim to distinguish effects of the two types of dynamics by choosing initial states as random product states from two factor spaces representing two subsystems.
Berry M V, Berry M V, Cartan E, Casati G, Flores J, French J B, Gorin T, Mehta M L, Mello P A, Prosen T, Seligman T H, T Gorin, T H Seligman   +12 more
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A random matrix approach to credit risk. [PDF]

PLoS ONE, 2014
We estimate generic statistical properties of a structural credit risk model by considering an ensemble of correlation matrices. This ensemble is set up by Random Matrix Theory.
Michael C Münnix, Rudi Schäfer, Thomas Guhr   +2 more
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