Representation theory and random point processes

Abstract

We discuss a connection between two areas of mathematics which until recently seemed to be rather distant from each other: (1) noncommutative harmonic analysis on groups and (2) some topics in probability theory related to random point processes. In order to make the paper accessible to readers not familiar with either of these areas, we explain all needed basic concepts. This is an extended version of G.Olshanski's talk at the 4th European Congress of Mathematics.

AMSTeX, 20 pages

References in corpus (3)

• Infinite random matrices and ergodic measures
• Z-Measures on partitions, Robinson-Schensted-Knuth correspondence, and beta=2 random matrix ensembles
• Point processes and the infinite symmetric group. Part III: Fermion point processes

Cited by in corpus (7)

• The Ginibre ensemble of real random matrices and its scaling limits
• Kerov's central limit theorem for Schur-Weyl measures of parameter 1/2
• Correlation Functions of Asymmetric Real Matrices
• Asymptotics of Plancherel measures for the infinite-dimensional unitary group
• Markov dynamics on the dual object to the infinite-dimensional unitary group
• Skew Howe duality and limit shapes of Young diagrams
• The Gelfand-Tsetlin graph and Markov processes