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 language | English |
|---|---|
| Pages (from-to) | 451-466 |
| Number of pages | 16 |
| Journal | Probability and Mathematical Statistics |
| Volume | 33 |
| Issue number | 2 |
| Publication status | Published - 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