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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