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.
Bibliographical noteFunding Information:
✩ The present research was partially conducted during the period the first named author (A.B.) served as a Clay Mathematics Institute Research Fellow; he was also partially supported by the NSF grant DMS-0402047 and the CRDF grant RIM1-2622-ST-04. The second named author (G.O.) was supported by the CRDF grant RM1-2543-MO-03. * Corresponding author. E-mail addresses: firstname.lastname@example.org (A. Borodin), email@example.com (G. Olshanski), firstname.lastname@example.org (E. Strahov).