Related papers: Symmetric functions and random partitions
These are a set of lecture notes on generalized global symmetries in quantum field theory. The focus is on invertible symmetries with a few comments regarding non-invertible symmetries. The main topics covered are the basics of higher-form…
This manuscript is essentially a collection of lecture notes which were given by the first author at the Summer School Wisl-2019, Poland and written down by the second author. As the title suggests, the material covered here includes the…
This note is an expansion of three lectures given at the workshop "Topology, Complex Analysis and Arithmetic of Hyperbolic Spaces" held at Kyoto University in December of 2006 and will appear in the proceedings for this workshop.
Random matrix theory has played a major role in several areas of pure and applied mathematics, as well as statistics, physics, and computer science. This lecture aims to describe the intrinsic freeness phenomenon and how it provides new…
In this short lecture, we compute asymptotics of orthogonal polynomials, from a saddle point approximation. This is an example of a calculation which shows the link between integrability, algebraic geometry and random matrices.
An asymptotic formula for the number of partitions into p-cores is derived. As a byproduct some integer valued trigonometric sums are found
Lecture script of a one-semester course that aims to develop an understanding and appreciation of fundemental concepts in modern physics for students who are comfortable with calculus. This document contains the last part of the course…
Although symmetry methods and analysis are a necessary ingredient in every physicist's toolkit, rather less use has been made of combinatorial methods. One exception is in the realm of Statistical Physics, where the calculation of the…
These notes are an expanded version of a short course of lectures given for graduate students in particle physics at Oxford. The level was intended to be appropriate for students in both experimental and theoretical particle physics.The…
Polysymmetric functions, introduced by Asvin G and Andrew O'Desky as a generalization of symmetric functions, have natural connections to algebraic geometry and provide a foundation for further developments. In this paper, we study…
Special functions have always played a central role in physics and in mathematics, arising as solutions of particular differential equations, or integrals, during the study of particular important physical models and theories in Quantum…
We provide, under minimal continuity assumptions, a description of \textsl{additive partition entropies}. They are real functions $I$ on the set of finite partitions that are additive on stochastically independent partitions in a given…
This article (written in Polish) is aimed for a wide mathematical audience. It is intended as an introductory text concerning problems of the asymptotic theory of symmetric groups.
These lecture notes provide an introduction to free probability theory, with a focus on tools and techniques useful in the study of large random matrices. Topics include freeness, free cumulants, additive and multiplicative free…
This paper is part of series on self-contained papers in which a large part, if not the full extent, of the asymptotic limit theory of summands of independent random variables is exposed. Each paper of the series may be taken as review…
Many asymptotic formulas exist for unrestricted integer partitions as well as for distinct partitions of integers into a finite number of parts. Szekeres and Canfield have derived an asymptotic formula for the number of partitions that is…
The study of partitions with parts separated by parity was initiated by Andrews in connection with Ramanujan's mock theta functions, and his variations on this theme have produced generating functions with a large variety of different…
Talk at the 25th Johns Hopkins Workshop "2001: A Relativistic Spacetime Odyssey", Firenze September 2001.
Motivated by connections with observable phenomena, in particular with soft factorization theorems for scattering amplitudes and with memory effects, renewed interest has been recently shown in the subject of asymptotic symmetries at null…
The dominant theme of this thesis is that random matrix valued analytic functions, generalizing both random matrices and random analytic functions, for many purposes can (and perhaps should) be effectively studied in that level of…