We link the appearance of universal kernels in random matrix ensembles to the phenomenon of shock formation in some fluid dynamical equations. Such equations are derived from Dyson's random walks after a proper rescaling of the time. In the case of the gaussian unitary ensemble, on which we focus in this paper, we show that the characteristics polynomials and their inverse evolve according to a...

This paper serves to prove the thesis that a computational trick can open entirely new approaches to theory. We illustrate by describing such random matrix techniques as the stochastic operator approach, the method of ghosts and shadows, and the method of “Riccatti Diffusion/Sturm Sequences,” giving new insights into the deeper mathematics underneath random matrix theory.

Despite the tremendous advancements in the field of network theory, very few studies have taken weights in the interactions into consideration that emerge naturally in all real world systems. Using random matrix analysis of a weighted social network, we demonstrate the profound impact of weights in interactions on emerging structural properties. The analysis reveals that randomness existing in ...

The tools currently available in each of these domains are not powerful enough alone to account for the diversity and complexity of content typical of real everyday life egocentric videos. Current maps, composed of meaningless geometric entities, are quite poor for performing high-level tasks such as object manipulation. Focusing on functional human activities (that often involve interactions w...

The neutron resonances, especially in heavy fissioning nuclei, were extensively studied during last 60 years. The renewed interest to their properties is related to the problem of quantum chaos. In the region of low neutron energies, the resonances are very narrow and well separated. The large lifetime and the small energy spread allow one to interpret a resonance as a fully equilibrated compou...

In this paper, we present several applications of recent results of large random matrix theory (RMT) to the performance analysis of small cell networks (SCNs). In a nutshell, SCNs are based on the idea of a very dense deployment of low-cost low-power base stations (BSs) that are substantially smaller than existing macro cell equipment. However, a massive network densification causes many new ch...

Random matrix theory is used to represent generic loss of coherence of a fixed central system coupled to a quantum-chaotic environment, represented by a random matrix ensemble, via random interactions. We study the average density matrix arising from the ensemble induced, in contrast to previous studies where the average values of purity, concurrence, and entropy were considered; we further dis...

This paper surveys the largest eigenvalue distributions appearing in random matrix theory and their application to multivariate statistical analysis.

Random matrix theory (RMT) is used to model the asymptotics of the discrete moments of the derivative of the Riemann zeta function, (s), evaluated at the complex zeros 1 2 + in, using the methods introduced by Keating and Snaith in 14]. We also discuss the probability distribution of ln j 0 (1=2 + in)j, proving the central limit theorem for the corresponding random matrix distribution and analy...

Neural network configurations with random weights play an important role in the analysis of deep learning. They define the initial loss landscape and are closely related to kernel and random feature methods. Despite the fact that these networks are built out of random matrices, the vast and powerful machinery of random matrix theory has so far found limited success in studying them. A main obst...