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
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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 -