Related papers: Random Matrix Theory and Classical Statistical Mec…
We study spectral behavior of sparsely connected random networks under the random matrix framework. Sub-networks without any connection among them form a network having perfect community structure. As connections among the sub-networks are…
We place ourselves in the setting of high-dimensional statistical inference, where the number of variables $p$ in a data set of interest is of the same order of magnitude as the number of observations $n$. More formally, we study the…
We study the distribution of entries of a random permutation matrix under a "randomized basis," i.e., we conjugate the random permutation matrix by an independent random orthogonal matrix drawn from Haar measure. It is shown that under…
Matrix Models are the most effective way to describe strongly interacting systems with many degrees of freedom. They have proven successful in describing very different settings, from nuclei spectra to conduction in mesoscopic systems, from…
We study an ensemble of random matrices (the Rosenzweig-Porter model) which, in contrast to the standard Gaussian ensemble, is not invariant under changes of basis. We show that a rather complete understanding of its level correlations can…
We discuss recently discovered links of the statistical models of normal random matrices to some important physical problems of pattern formation and to the quantum Hall effect. Specifically, the large $N$ limit of the normal matrix model…
These lecture notes are a concise introduction of recent techniques to prove local spectral universality for a large class of random matrices. The general strategy is presented following the recent book with H.T. Yau. We extend the scope of…
The statistical model proposed in an accompanying paper is generalized to treat multiport scattering problems. Attention is first focused on two-port lossless systems and the model is shown to be consistent with Random Matrix Theory. The…
We present most general one-parametric solutions of the Yang-Baxter equations (YBE) for one spectral parameter dependent $R_{ij}(u)$-matrices of the six- and eight-vertex models, where the only constraint is the particle number conservation…
We propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted…
We apply random matrix theory to complex networks. We show that nearest neighbor spacing distribution of the eigenvalues of the adjacency matrices of various model networks, namely scale-free, small-world and random networks follow…
Starting with the average particle distribution function for bosons and fermions for non-extensive thermodynamics , as proposed in \cite{CMP}, we obtain the corresponding density matrix operators and hamiltonians. In particular, for the…
Random matrix theory is a well-developed area of probability theory that has numerous connections with other areas of mathematics and its applications. Much of the literature in this area is concerned with matrices that possess many exact…
This paper considers the problem of testing for latent structure in large symmetric data matrices. The goal here is to develop statistically principled methodology that is flexible in its applicability, computationally efficient, and…
In this paper we investigate trigonometric vertex models associated with solutions of the Yang-Baxter equation which are invariant relative to q-deformed superalgebras sl(r|2m)^(2), osp(r|2m)^(1) and osp(r=2n|2m)^(2). The associated…
We introduce and solve exactly a family of invariant 2x2 random matrices, depending on one parameter \eta, and we show that rotational invariance and real Dyson index \beta are not incompatible properties. The probability density for the…
We present an intuitive diagrammatic representation of a new class of integrable $\s$-models. It is shown that to any given diagram corresponds an integrable theory that couples $N$ WZW models with a certain number of each of the following…
This thesis deals with a class of integrable field theories called models with twist function. The main examples of such models are integrable non-linear sigma models, such as the Principal Chiral Model, and their deformations. A first…
A review of some recent results on the dynamical theory of the Yang-Baxter maps (also known as set-theoretical solutions to the quantum Yang-Baxter equation) is given. The central question is the integrability of the transfer dynamics. The…
By randomly removing a fraction of levels from a given spectrum a model is constructed that describes a crossover from this spectrum to a Poisson spectrum. The formalism is applied to the transitions towards Poisson from random matrix…