Orthogonal Stochastic Duality Functions from Lie Algebra Representations

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Abstract

We obtain stochastic duality functions for specific Markov processes using representation theory of Lie algebras. The duality functions come from the kernel of a unitary intertwiner between ∗-representations, which provides (generalized) orthogonality relations for the duality functions. In particular, we consider representations of the Heisenberg algebra and su(1,1). Both cases lead to orthogonal (self-)duality functions in terms of hypergeometric functions for specific interacting particle processes and interacting diffusion processes.
Original languageEnglish
Pages (from-to)97-119
Number of pages23
JournalJournal of Statistical Physics
Volume174
Issue number1
DOIs
Publication statusPublished - 2019

Keywords

  • Stochastic duality
  • Lie algebra representations
  • Hypergeometric functions
  • Orthogonal polynomials

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