Mutually avoiding paths in random media and largest eigenvalues of random matrices. by De Luca, A, Le Doussal, P

“…The latter describes the fluctuations of the largest eigenvalue of a random matrix, drawn from the Gaussian unitary ensemble (GUE), and the result holds for a DP with fixed end points, i.e., for the KPZ equation with droplet initial conditions. …”

Extreme values of CUE characteristic polynomials: a numerical study by Fyodorov, Y, Gnutzmann, S, Keating, J

“…We present the results of systematic numerical computations relating to the extreme value statistics of the characteristic polynomials of random unitary matrices drawn from the circular unitary ensemble (CUE) of random matrix theory. In particular, we investigate a range of recent conjectures and theoretical results inspired by analogies with the theory of logarithmically-correlated Gaussian random fields. …”

Weak chaos and mixed dynamics in the string S-matrix by Nikola Savić, Mihailo Čubrović

“…Only for special values of momenta and (for photon scattering) scattering angles do we find strong chaos of random matrix type. These special values correspond to a crossover between two regimes of scattering, dominated by short versus long partitions of the total occupation number of the highly excited string; they also maximize the information entropy of the S-matrix. …”
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Symmetry violation of quantum multifractality: Gaussian fluctuations versus algebraic localization by A. M. Bilen, B. Georgeot, O. Giraud, G. Lemarié, I. García-Mata

“…The first one was already known and is related to Gaussian fluctuations well described by random matrix theory. The second one, not previously explored, is related to the presence of an algebraically localized envelope. …”
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New pattern in regular nuclei based on their experimental quadrupole transition rates and some new candidates by Asgar Hosseinnezhad, Masoud Seidi, Hadi Sabri

“…In order to further study the statistical distribution of experimental energy levels related to the electromagnetic transitions we are considering, we studied using the random matrix theory. The results confirmed their regularity.…”
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Epidemic thresholds and human mobility by Marta Pardo-Araujo, David García-García, David Alonso, Frederic Bartumeus

“…Here, we propose a flexible modelling framework that brings conclusions about the influence of human mobility and disease transmission on early epidemic growth, with applicability in outbreak preparedness. We use random matrix theory to compute an epidemic threshold, equivalent to the basic reproduction number $$R_{0}$$ R 0 , for a SIR metapopulation model. …”
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Spacing ratio statistics of multiplex directed networks by Tanu Raghav, Sarika Jalan

“…Eigenvalues statistics of various many-body systems have been widely studied using the nearest neighbor spacing distribution under the random matrix theory framework. Here, we numerically analyze eigenvalue ratio statistics of multiplex networks consisting of directed Erdős-Rényi random networks layers represented as, first, weighted non-Hermitian random matrices and then weighted Hermitian random matrices. …”
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Chaotic Zeeman effect: a fractional diffusion-like approch by Octavian Postavaru, Mariana M. Stanescu

“…Considering a Lorenzian type distribution, we can make a connection between the fractional formalism and random matrix theory. The connection validates the link between fractional calculus and chaos, and at the same time due to the $$\theta $$ θ angle, it gives the phenomenon a physical interpretation.…”
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Spectral statistics of chaotic many-body systems by Rémy Dubertrand, Sebastian Müller

“…We show that in the limits taken the statistics of fully chaotic many-particle systems becomes universal and agrees with predictions from the Wigner–Dyson ensembles of random matrix theory. The conditions for Wigner–Dyson statistics involve a gap in the spectrum of the Frobenius–Perron operator, leaving the possibility of different statistics for systems with weaker chaotic properties.…”
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Cognitive Spectrum Sensing with Multiple Primary Users in Rayleigh Fading Channels by Salam Al-Juboori, Sattar J. Hussain, Xavier Fernando

“…Among many techniques, recently proposed eigenvalue-based detectors that use random matrix theories to eliminate the need of prior knowledge of the signals proved to be a solid approach. …”
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Hydrodynamics of disordered marginally stable matter by Matteo Baggioli, Alessio Zaccone

“…We compare our results with numerical simulations data and random matrix theory. Finally, we compute the specific heat and we show the existence of a linear in T scaling C(T)∼cT at low temperatures due to the diffusive modes. …”
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The Sufficient Conditions for Orthogonal Matching Pursuit to Exactly Reconstruct Sparse Polynomials by Aitong Huang, Renzhong Feng, Andong Wang

“…Then, based on a more accurate estimation of the mutual coherence of a structured random matrix, the recovery guarantees and success probabilities for OMP to reconstruct sparse polynomials are obtained with the help of those sufficient conditions. …”
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The functional generalization of the Boltzmann-Vlasov equation and its gauge-like symmetry by Giorgio Torrieri

“…When causality and Lorentz invariance are omitted this problem can be look at via random matrix theory show, and we show that in such a case thermalization happens much more quickly than the Boltzmann equation would infer. …”
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Strong ergodicity breaking due to local constraints in a quantum system by Sthitadhi Roy, Achilleas Lazarides

“…We support this picture by introducing and solving numerically a class of random matrix models that retain the bottlenecks. Finally, we obtain analytical insight into the origins of localization using the forward-scattering approximation. …”
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Singular-Value Statistics of Non-Hermitian Random Matrices and Open Quantum Systems by Kohei Kawabata, Zhenyu Xiao, Tomi Ohtsuki, Ryuichi Shindou

“…Furthermore, we demonstrate that singular values of open quantum many-body systems follow the random-matrix statistics, thereby identifying chaos and nonintegrability in open quantum systems. …”
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Analyticity constraints bound the decay of the spectral form factor by Pablo Martinez-Azcona, Aurélia Chenu

“…The results are illustrated in systems with regular, chaotic, and tunable dynamics, namely the single-particle harmonic oscillator, the many-particle Calogero-Sutherland model, an ensemble from random matrix theory, and the quantum kicked top. The relation of the derived bound with other known bounds, including quantum speed limits, is discussed.…”
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General β-Jacobi Corners Process and the Gaussian Free Field by Borodin, Alexei, Gorin, Vadim

“…We prove that the two-dimensional Gaussian free field describes the asymptotics of global fluctuations of a multilevel extension of the general β-Jacobi random matrix ensembles. Our approach is based on the connection of the Jacobi ensembles to a degeneration of the Macdonald processes that parallels the degeneration of the Macdonald polynomials to the Heckman-Opdam hypergeometric functions (of type A). …”
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The logarithmic law of random determinant by Bao, Zhigang, Pan, Guangming, Zhou, Wang

“…Consider the square random matrix An=(aij)n,n, where {aij:=a(n)ij,i,j=1,…,n} is a collection of independent real random variables with means zero and variances one.…”
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Ranking and synchronization from pairwise measurements via SVD by d'Aspremont, A, Cucuringu, M, Tyagi, H

“…We provide a detailed theoretical analysis in terms of robustness against both sampling sparsity and noise perturbations with outliers, using results from matrix perturbation and random matrix theory. Our theoretical findings are complemented by a detailed set of numerical experiments on both synthetic and real data, showcasing the competitiveness of our proposed algorithms with other state-of-the-art methods.…”

On tail decay and moment estimates of a condition number for random linear conic systems by Cheung, D, Cucker, F, Hauser, R

“…We consider the case where this system is defined by a Gaussian random matrix and characterise the exact decay rates of the distribution tails, improve the existing moment estimates, and prove various limit theorems for large scale systems. …”