Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random Walkers with Shrinking Steps in d-Dimensions and Their Long Term
  Memory   We study, in d-dimensions, the random walker with geometrically shrinking
step sizes at each hop. We emphasize the integrated quantities such as
expectation values, cumulants and moments rather than a direct study of the
probability distribution. We develop a 1/d expansion technique and study
various correlations of the first step to the position as ti me goes to
infinity. We also show and substantiate with a study of the cumulants that to
order 1/d the system admits a continuum counterpart equation which can be
obtained with a generalization of the ordinary technique to obtain the
continuum limit. We also advocate that this continuum counterpart equation,
which is nothing but the ordinary diffusion equation with a diffusion constant
decaying exponentially in continuous time, captures all the qualitative aspects
of t he discrete system and is often a good starting point for quantitative
approximations.

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The categories of this paper are: physics
31
The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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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: cs
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: eess