TY - JOUR

T1 - One-mode interacting Fock spaces and random walks on graphs

AU - Obata, Nobuaki

PY - 2012/4

Y1 - 2012/4

N2 - 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.

AB - 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.

KW - Accardi-Bożejko formula

KW - interacting Fock space

KW - Karlin-McGregor formula

KW - orthogonal polynomials

KW - random walk

UR - http://www.scopus.com/inward/record.url?scp=84860316512&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84860316512&partnerID=8YFLogxK

U2 - 10.1080/17442508.2010.550919

DO - 10.1080/17442508.2010.550919

M3 - Article

AN - SCOPUS:84860316512

SN - 1744-2508

VL - 84

SP - 383

EP - 392

JO - Stochastics

JF - Stochastics

IS - 2-3

ER -