Determinantal point processes from symplectic and orthogonal characters and applications
Probability
2020-01-31 v1 Mathematical Physics
Combinatorics
math.MP
Representation Theory
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 Szeg\H{o}-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.
Cite
@article{arxiv.2001.11260,
title = {Determinantal point processes from symplectic and orthogonal characters and applications},
author = {Dan Betea},
journal= {arXiv preprint arXiv:2001.11260},
year = {2020}
}
Comments
10 pages; extended abstract version based largely on arXiv:1804.08495 [math-ph]; Theorem 6 is new