Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite time and asymptotic behaviour of the maximal excursion of a
  random walk   We evaluate the limit distribution of the maximal excursion of a random walk
in any dimension for homogeneous environments and for self-similar supports
under the assumption of spherical symmetry. This distribution is obtained in
closed form and is an approximation of the exact distribution comparable to
that obtained by real space renormalization methods. Then we focus on the early
time behaviour of this quantity. The instantaneous diffusion exponent $\nu_n$
exhibits a systematic overshooting of the long time exponent. Exact results are
obtained in one dimension up to third order in $n^{-1/2}$. In two dimensions,
on a regular lattice and on the Sierpi\'nski gasket we find numerically that
the analytic scaling $\nu_n \simeq \nu+A n^{-\nu}$ holds.

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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph