Séminaire Lotharingien de Combinatoire, 84B.41 (2020), 12 pp.

Dan Betea

Determinantal Point Processes from Symplectic and Orthogonal Characters and Applications

Abstract. We show that the symplectic and orthogonal character analogues of Okounkov's Schur measure (on integer partitions) are determinantal, with explicit correlation kernels. We apply this to prove certain Borodin-Okounkov-Gessel-type results concerning Toeplitz+Hankel and Fredholm determinants; a Szegő-type limit theorem; an edge Baik-Deift-Johansson-type asymptotical result for certain symplectic and orthogonal analogues of the poissonized Plancherel measure; and a similar result for actual poissonized Plancherel measures supported on "almost symmetric" partitions.


Received: November 20, 2019. Accepted: February 20, 2020. Final version: April 30, 2020.

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