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Self-similarity and spectral asymptotics for the continuum random tree
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Croydon, David A. and Hambly, Ben M. (2008) Self-similarity and spectral asymptotics for the continuum random tree. Stochastic Processes and their Applications, Vol.118 (No.5). pp. 730-754. doi:10.1016/j.spa.2007.06.005 ISSN 0304-4149.
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Official URL: http://dx.doi.org/10.1016/j.spa.2007.06.005
Abstract
We use the random self-similarity of the continuum random tree to show that it is homeomorphic to a post-critically finite self-similar fractal equipped with a random self-similar metric. As an application, we determine the mean and almost-sure leading order behaviour of the high frequency asymptotics of the eigenvalue counting function associated with,the natural Dirichlet form on the continuum random tree. We also obtain short time asymptotics for the trace of the heat semigroup and the annealed on-diagonal heat kernel associated with this Dirichlet form. (c) 2007 Elsevier B.V. All rights reserved.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Library of Congress Subject Headings (LCSH): | Self-similar processes, Fractals, Continuum (Mathematics), Trees (Graph theory), Spectral theory (Mathematics), Asymptotic expansion | ||||
Journal or Publication Title: | Stochastic Processes and their Applications | ||||
Publisher: | Elsevier Science BV | ||||
ISSN: | 0304-4149 | ||||
Official Date: | May 2008 | ||||
Dates: |
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Volume: | Vol.118 | ||||
Number: | No.5 | ||||
Number of Pages: | 25 | ||||
Page Range: | pp. 730-754 | ||||
DOI: | 10.1016/j.spa.2007.06.005 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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