Unimodularity for multi-type Galton-Watson trees

作者：Altok Serdar^*

来源：Bernoulli, 2013, 19(3): 780-802.

DOI：10.3150/11-BEJ416

Fix n is an element of N. Let T-n be the set of rooted trees (T, o) whose vertices are labeled by elements of {1, ..., n}. Let nu be a strongly connected multi-type Galton-Watson measure. We give necessary and sufficient conditions for the existence of a measure mu, that is reversible for simple random walk on T-n and has the property that given the labels of the root and its neighbors, the descendant subtrees rooted at the neighbors of the root are independent multi-type Galton-Watson trees with conditional offspring distributions that are the same as the conditional offspring distributions of nu when the types are nu are ordered pairs of elements of [n]. If the types of nu are given by the labels of vertices, then we give an explicit description of such mu.

• 出版日期2013-8