One-mode interacting Fock spaces and random walks on graphs

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4 Citations (Scopus)


A one-mode interacting Fock space is reformulated in a slightly generalized form in terms of a tridiagonal matrix. We derive the continued fraction expansion of its resolvent and the combinatorial part of the Accardi-Bożejko formula. Under certain positivity condition, a probability distribution on the real line is related and the Karlin-McGregor formula is reproduced under slightly weaker conditions. We show concrete computation for random walks on graphs, e.g. the free Meixner law is derived from a random walk on a spidernet.

Original languageEnglish
Pages (from-to)383-392
Number of pages10
Issue number2-3
Publication statusPublished - 2012 Apr


  • Accardi-Bożejko formula
  • interacting Fock space
  • Karlin-McGregor formula
  • orthogonal polynomials
  • random walk


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