The uses of random partitions
arXiv:math-ph/0309015
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.
36 pages, 10 figures
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Cited by in corpus (15)
- Gaussian fluctuations of Young diagrams and structure constants of Jack characters
- Character expansion method for the first order asymptotics of a matrix integral
- Random surfaces enumerating algebraic curves
- On Kerov polynomials for Jack characters
- Random partitions and instanton counting
- Structure coefficients for Jack characters: approximate factorization property
- Random strict partitions and random shifted tableaux
- Quantum crystals, Kagome lattice and plane partitions fermion-boson duality
- Correlation functions of the shifted Schur measure
- The top-degree part in the Matchings-Jack Conjecture
- A probabilistic interpretation of the Macdonald polynomials
- Bijection between oriented maps and weighted non-oriented maps
- Jack deformations of Plancherel measures and traceless Gaussian random matrices
- Towards Yang-Baxter integrability of quantum crystal melting: From Kagome lattice to vertex models
- Periodic Schur process and cylindric partitions