One-mode interacting Fock spaces and random walks on graphs
One-mode interacting Fock spaces and random walks on graphs
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DOI：
10.1080/17442508.2010.550919
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发表时间：
2012-04
期刊：
影响因子：
--
通讯作者：
N. Obata
中科院分区：
文献类型：
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作者：
N. Obata
用三对角矩阵将单模相互作用Fock空间的形式稍微推广。我们推导出了其预解式的连分式展开式和Accardi-Boejko公式的组合部分。在一定的正性条件下，给出了真实的直线上的概率分布，并在较弱的条件下重现了Karlin-McGregor公式。我们显示具体的计算图上的随机游走，例如，自由的Meixner法是来自随机行走的蜘蛛网。
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.