Open AccessBrownian motion on ℝ-trees
Author(s) -
Siva Athreya,
Michael Eckhoff,
Anita Winter
Publication year - 2012
Publication title -
transactions of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.798
H-Index - 100
eISSN - 1088-6850
pISSN - 0002-9947
DOI - 10.1090/s0002-9947-2012-05752-7
Subject(s) - algorithm , annotation , artificial intelligence , type (biology) , mathematics , computer science , biology , ecology
The real trees form a class of metric spaces that extends the class of trees with edge lengths by allowing behavior such as locally 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 \mathbb {R} -tree ( T , r ) (T,r) equipped with a Radon measure ν \nu on ( T , B ( T ) ) (T,{\mathcal B}(T)) . We specify a criterion under which the Brownian motion is recurrent or transient. For compact recurrent R \mathbb {R} -trees we provide bounds on the mixing time.