The uses of random partitions

TL;DR

This paper explores the fundamental role of random partitions across various mathematical contexts, discussing their measures, correlation functions, limit shapes, and applications in advanced theories like Gromov-Witten and Seiberg-Witten.

Contribution

It provides a comprehensive overview of the natural measures and applications of random partitions in different mathematical and physical theories.

Findings

Analysis of measures on partitions

Discussion of correlation functions and limit shapes

Applications in Gromov-Witten and Seiberg-Witten theories

Abstract

These are extended notes for my talk at the ICMP 2003 in Lisbon. Our goal here is to demonstrate how natural and fundamental random partitions are from many different points of view. We discuss various natural measures on partitions, their correlation functions, limit shapes, and how they arise in applications, in particular, in the Gromov-Witten and Seiberg-Witten theory.