Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral asymptotics for stable trees   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.

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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: physics
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The categories of this paper are: bayes-an