Giambelli compatible point processes

Alexei Borodin, Grigori Olshanski, Eugene Strahov

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)

Abstract

We distinguish a class of random point processes which we call Giambelli compatible point processes. Our definition was partly inspired by determinantal identities for averages of products and ratios of characteristic polynomials for random matrices found earlier by Fyodorov and Strahov. It is closely related to the classical Giambelli formula for Schur symmetric functions. We show that orthogonal polynomial ensembles, z-measures on partitions, and spectral measures of characters of generalized regular representations of the infinite symmetric group generate Giambelli compatible point processes. In particular, we prove determinantal identities for averages of analogs of characteristic polynomials for partitions. Our approach provides a direct derivation of determinantal formulas for correlation functions.

Original languageEnglish
Pages (from-to)209-248
Number of pages40
JournalAdvances in Applied Mathematics
Volume37
Issue number2
DOIs
Publication statusPublished - Aug 2006
Externally publishedYes

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