Brownian motion on R trees

Athreya, Siva ; Eckhoff, Michael ; Winter, Anita (2013) Brownian motion on R trees Transactions of the American Mathematical Society, 365 . pp. 3115-3150. ISSN 0002-9947

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The real trees form a class of metric spaces that extends the class of trees with edge lengths by allowing behavior such as infinite total edge length and vertices with infinite branching degree. We use Dirichlet form methods to construct Brownian motion on any given locally compact R-tree (T,r) equipped with a Radon measure ν on (T,B(T)). We specify a criterion under which the Brownian motion is recurrent or transient. For compact recurrent R-trees we provide bounds on the mixing time.

Item Type:Article
Source:Copyright of this article belongs to American Mathematical Society.
Keywords:R-trees; Brownian Motion; Diffusions on Metric Measure Trees; Dirichlet Forms; Spectral Gap; Mixing Times; Recurrence
ID Code:100046
Deposited On:12 Feb 2018 12:16
Last Modified:12 Feb 2018 12:16

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