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Mathematical Physics

arXiv:1804.08495 (math-ph)
[Submitted on 23 Apr 2018 (v1), last revised 18 Jun 2018 (this version, v2)]

Title:Correlations for symplectic and orthogonal Schur measures

Authors:Dan Betea
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Abstract:We show, using either Fock space techniques or Macdonald difference operators, that certain symplectic and orthogonal analogues of Okounkov's Schur measure are determinantal with kernels given by explicit double contour integrals. We give two applications: one equates certain Toeplitz+Hankel determinants of random matrix theory with appropriate Fredholm determinants and computes Szegő asymptotics for the former; another finds that the simplest examples of said measures exhibit discrete sine kernel asymptotics in the bulk and Airy 2 to 1 kernel---along with a certain dual---asymptotics at the edge. We believe the edge behavior to be universal.
Comments: 23 pages; minor edits compared to v1: added more details in proof of Thm 4, slightly altered the abstract, changed \tilde and \check notation so the former agrees with the literature, changed awkward indexing of Toeplitz+Hankel determinants, corrected typos and other minor errors
Subjects: Mathematical Physics (math-ph); Combinatorics (math.CO); Probability (math.PR); Representation Theory (math.RT)
Cite as: arXiv:1804.08495 [math-ph]
  (or arXiv:1804.08495v2 [math-ph] for this version)
  https://doi.org/10.48550/arXiv.1804.08495

Submission history

From: Dan Betea [view email]
[v1] Mon, 23 Apr 2018 15:16:20 UTC (32 KB)
[v2] Mon, 18 Jun 2018 15:25:18 UTC (32 KB)
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