Hard-edge asymptotics of the Jacobi growth process

Mark Cerenzia, Jeffrey Kuan

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We introduce a two parameter (a,β > -1) family of interacting particle systems with determinantal correlation kernels expressible in terms of Jacobi polynomials {P(a,β)k } k=0. The family includes previously discovered Plancherel measures for the infinite-dimensional orthogonal and symplectic groups. The construction uses certain multivariate BC-type orthogonal polynomials that generalize the characters of these groups. The local asymptotics near the hard edge where one expects distinguishing behavior yields the multi-time (a,β)-dependent discrete Jacobi kernel and the multi-time β-dependent hard-edge Pearcey kernel. The hard-edge Pearcey kernel has previously appeared in the asymptotics of non-intersecting squared Bessel paths at the hard edge.

Original languageEnglish (US)
Pages (from-to)2329-2355
Number of pages27
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume56
Issue number4
DOIs
StatePublished - Nov 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Determinantal point process
  • Hard-edge Pearcey
  • Jacobi

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