Universality for mathematical and physical systems

Abstract

All physical systems in equilibrium obey the laws of thermodynamics. In other words, whatever the precise nature of the interaction between the atoms and molecules at the microscopic level, at the macroscopic level, physical systems exhibit universal behavior in the sense that they are all governed by the same laws and formulae of thermodynamics. In this paper we describe some recent history of universality ideas in physics starting with Wigner's model for the scattering of neutrons off large nuclei and show how these ideas have led mathematicians to investigate universal behavior for a variety of mathematical systems. This is true not only for systems which have a physical origin, but also for systems which arise in a purely mathematical context such as the Riemann hypothesis, and a version of the card game solitaire called patience sorting.

New version contains some additional explication of the problems considered in the text and additional references

References in corpus (1)

• A simple invariance theorem

Cited by in corpus (5)

• Fluctuation properties of the TASEP with periodic initial configuration
• High Dimensional Statistical Inference and Random Matrices
• The universal Airy_1 and Airy_2 processes in the Totally Asymmetric Simple Exclusion Process
• Edgeworth Expansion of the Largest Eigenvalue Distribution Function of GUE Revisited
• From the Littlewood-Offord problem to the Circular Law: universality of the spectral distribution of random matrices