相关论文: Symmetry classes in random matrix theory

It is known that hermitean random matrix ensembles can be identified with symmetric coset spaces of Lie groups, or else with tangent spaces of the same. This results in a classification of random matrix ensembles as well as applications in…

The random permutation is the Fra\"iss\'e limit of the class of finite structures with two linear orders. Answering a problem stated by Peter Cameron in 2002, we use a recent Ramsey-theoretic technique to show that there exist precisely 39…

We show that, in contrast to classical random graph models, many real-world complex systems -- including a variety of biological regulatory networks and technological networks such as the internet -- spontaneously self-organize to a richly…

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…

In recent years, random matrices have come to play a major role in computational mathematics, but most of the classical areas of random matrix theory remain the province of experts. Over the last decade, with the advent of matrix…

Mathematical models play an increasingly important role in the interpretation of biological experiments. Studies often present a model that generates the observations, connecting hypothesized process to an observed pattern. Such generative…

This paper is my contribution to the planned publication Recent Perspectives in Random Matrix Theory (Cambridge University Press). Addressed is the problem of computing spacing distributions in the bulk for the three symmetry classes…

Symmetry is a fundamental tool in the exploration of a broad range of complex systems. In machine learning symmetry has been explored in both models and data. In this paper we seek to connect the symmetries arising from the architecture of…

Symmetry can be used to help solve many problems. For instance, Einstein's famous 1905 paper ("On the Electrodynamics of Moving Bodies") uses symmetry to help derive the laws of special relativity. In artificial intelligence, symmetry has…

We introduce a class of o.d.e.'s that generalizes to polymatrix games the replicator equations on symmetric and asymmetric games. We also introduce a new class of Poisson structures on the phase space of these systems, and characterize the…

An equivalence relation in the symmetric group, where is a positive integer has been considered. An algorithm for calculation of the number of the equivalence classes by this relation for arbitrary integer has been described.

Some tools and ideas are interchanged between random matrix theory and multivariate statistics. In the context of the random matrix theory, classes of spherical and generalised Wishart random matrix ensemble, containing as particular cases…

A unified classification and analysis is presented of two dimensional Dirac operators of QCD-like theories in the continuum as well as in a naive lattice discretization. Thereby we consider the quenched theory in the strong coupling limit.…

The statistical properties of spectra of quantum systems within the framework of random matrix theory is widely used in many areas of physics. These properties are affected, if two or more sets of spectra are superposed, resulting from the…

The problem of diagonalizing hermitian matrices of continuous fiunctions was studied by Grove and Pederson in 1984. While diagonalization is not possible in general, in the presence of differentiability conditions we are able to obtain…

We analyze statistical properties of the complex system with conditions which manifests through specific constraints on the column/row sum of the matrix elements. The presence of additional constraints besides symmetry leads to new…

This is a course on Random Matrix Theory which includes traditional as well as advanced topics presented with an extensive use of classical logarithmic plasma analogy and that of the quantum systems of one-dimensional interacting fermions…

Discrete (family) symmetries might play an important role in models of elementary particle physics. We discuss the origin of such symmetries in the framework of consistent ultraviolet completions of the standard model in field and string…

We numerically analyze the random matrix ensembles of real-symmetric matrices with column/row constraints for many system conditions e.g. disorder type, matrix-size and basis-connectivity. The results reveal a rich behavior hidden beneath…

The problem of classification into symmetry integrable classes is solved for a family of second order nonlinear evolution equations labeled by arbitrary functions. Four nonequivalent symmetry integrable classes are thus obtained and the…