相关论文: Developments in Random Matrix Theory
Matrices are very popular and widely used in mathematics and other fields of science. Every mathematician has known the properties of finite-sized matrices since the time of study. In this paper, we consider the basic theory of infnite…
In this presentation, I will summarize the present status of the developments with a Universal Theory of Relativity \cite{smw-utr}. Some general challenges to be overcome will also be discussed.
The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. At the same time many recent applications from convex geometry to functional analysis to…
This is a brief description of what has been accomplished and what remains to be done in the construction of a nonperturbative formulation of "The Theory Formerly Known as String". It is culled from two short talks given by the author at…
In this talk an introduction to generalized parton distributions is given. Recent developments are shortly reviewed, including non-perturbative calculations, phenomenological aspects and evaluation of higher order perturbative and power…
I briefly discuss some recent developments (and recall some old news) in the theory and phenomenology of generalised parton distributions.
This chapter is an introduction to the connection between random matrices and maps, i.e graphs drawn on surfaces. We concentrate on the one-matrix model and explain how it encodes and allows to solve a map enumeration problem.
We provide a self-contained introduction to random matrices. While some applications are mentioned, our main emphasis is on three different approaches to random matrix models: the Coulomb gas method and its interpretation in terms of…
The aim of this paper is to study some aspects of matrix theory through Pasting and Reversing. We start giving a summary of previous results concerning to Pasting and Reversing over vectors and matrices, after we rewrite such properties of…
This is an introduction to advanced linear algebra, with emphasis on geometric aspects, and with some applications included too. We first review basic linear algebra, notably with the spectral theorem in its general form, and with the…
This is an informal discussion on one of the basic problems in the theory of empirical processes, addressed in our preprint "Combinatorics of random processes and sections of convex bodies", which is available at ArXiV and from our web…
Brief review of concepts and unsolved problems in the theory of matrix models.
Supersymmetry is nowadays indispensable for many problems in Random Matrix Theory. It is presented here with an emphasis on conceptual and structural issues. An introduction to supermathematics is given. The Hubbard-Stratonovich…
This PhD thesis deals with a number of different problems in mathematical physics with the common thread that they have probabilistic aspects. The problems all stem from mathematical studies of lattice systems in statistical and quantum…
This is survey of some recent results connecting random matrices, non-colliding processes and queues.
An informal guide to the history of Heisenberg's matrix mechanics. It is designed for mathematicians with only a minimal background in either physics or geometry, and it is based upon Heisenberg's original arguments.
A didactical survey of the foundations of Algorithmic Information Theory. These notes are short on motivation, history and background but introduce some of the main techniques and concepts of the field. The "manuscript" has been evolving…
Uncertainty, characterised by randomness and stochasticity, is ubiquitous in applications of evolutionary game theory across various fields, including biology, economics and social sciences. The uncertainty may arise from various sources…
We propose a random matrix modeling for the parametric evolution of eigenstates. The model is inspired by a large class of quantized chaotic systems. Its unique feature is having parametric invariance while still possessing the…
Matrix models are a promising candidate for a nonperturbative formulation of the superstring theory. It is possible to study how the standard model and other phenomenological models appear from the matrix model, and estimate the probability…