The Karlin-McGregor formula for paths connected with a clique

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Abstract

The Karlin-McGregor formula, a well-known integral expression of the m-step transition probability for a nearest-neighbor random walk on the non-negative integers (an infinite path graph), is reformulated in terms of one-mode interacting Fock spaces. A truncated direct sum of one-mode interacting Fock spaces is newly introduced and an integral expression for the m-th moment of the associated operator is derived. This integral expression gives rise to an extension of the Karlin-McGregor formula to the graph of paths connected with a clique.

Original languageEnglish
Pages (from-to)451-466
Number of pages16
JournalProbability and Mathematical Statistics
Volume33
Issue number2
Publication statusPublished - 2013 Dec 12

Keywords

  • Jacobi matrix
  • Karlin-McGregor formula
  • Kesten distribution
  • One-mode interacting Fock space
  • Orthogonal polynomials
  • Tridiagonal matrix

ASJC Scopus subject areas

  • Statistics and Probability

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