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Spectral Asymptotics for Stable Trees

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Spectral Asymptotics for Stable Trees
2.	Creator	Author's name, affiliation, country	David A Croydon; University of Warwick; United Kingdom
2.	Creator	Author's name, affiliation, country	Benjamin M Hambly; University of Oxford; United Kingdom
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	stable tree; self-similar decomposition; spectral asymptotics; heat kernel
3.	Subject	Subject classification	35P20; 28A80; 58G25; 60J35; 60J80
4.	Description	Abstract	We calculate 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 $\alpha$-stable trees, which lead in turn to short-time heat kernel asymptotics for these random structures. In particular, the conclusions we obtain demonstrate that the spectral dimension of an $\alpha$-stable tree is almost-surely equal to $2\alpha/(2\alpha-1)$, matching that of certain related discrete models. We also show that the exponent for the second term in the asymptotic expansion of the eigenvalue counting function is no greater than $1/(2\alpha-1)$. To prove our results, we adapt a self-similar fractal argument previously applied to the continuum random tree, replacing the decomposition of the continuum tree at the branch point of three suitably chosen vertices with a recently developed spinal decomposition for $\alpha$-stable trees
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2010-11-14
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/819
10.	Identifier	Digital Object Identifier	10.1214/EJP.v15-819
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 15
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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