Brownian motion on $\mathbb {R}$-trees
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- by Siva Athreya, Michael Eckhoff and Anita Winter PDF
- Trans. Amer. Math. Soc. 365 (2013), 3115-3150 Request permission
Abstract:
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 $\mathbb {R}$-tree $(T,r)$ equipped with a Radon measure $\nu$ on $(T,{\mathcal B}(T))$. We specify a criterion under which the Brownian motion is recurrent or transient. For compact recurrent $\mathbb {R}$-trees we provide bounds on the mixing time.References
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Additional Information
- Siva Athreya
- Affiliation: Indian Statistical Institute, 8th Mile Mysore Road, Bangalore 560059, India
- Email: athreya@isibang.ac.in
- Anita Winter
- Affiliation: Fakultät für Mathematik, Universität Duisburg-Essen, Universitätsstrasse 2, 45141 Essen, Germany
- Email: anita.winter@uni-due.de
- Received by editor(s): October 13, 2011
- Published electronically: December 26, 2012
- Additional Notes: The first author was supported in part by a CSIR Grant in Aid scheme and Homi Bhaba Fellowship.
The third author was supported in part at the Technion by a fellowship from the Aly Kaufman Foundation - © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 365 (2013), 3115-3150
- MSC (2010): Primary 60B05, 60J60; Secondary 60J25, 60B99
- DOI: https://doi.org/10.1090/S0002-9947-2012-05752-7
- MathSciNet review: 3034461