Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random walk on the simple symmetric exclusion process   We investigate the long-term behavior of a random walker evolving on top of
the simple symmetric exclusion process (SSEP) at equilibrium, in dimension one.
  At each jump, the random walker is subject to a drift that depends on whether
it is sitting on top of a particle or a hole, so that its asymptotic behavior
is expected to depend on the density $\rho \in [0, 1]$ of the underlying SSEP.
  Our first result is a law of large numbers (LLN) for the random walker for
all densities $\rho$ except for at most two values $\rho_-, \rho_+ \in [0, 1]$.
  The asymptotic speed we obtain in our LLN is a monotone function of $\rho$.
  Also, $\rho_-$ and $\rho_+$ are characterized as the two points at which the
speed may jump to (or from) zero.
  Furthermore, for all the values of densities where the random walk
experiences a non-zero speed, we can prove that it satisfies a functional
central limit theorem (CLT).
  For the special case in which the density is $1/2$ and the jump distribution
on an empty site and on an occupied site are symmetric to each other, we prove
a LLN with zero limiting speed.
  Finally, we prove similar LLN and CLT results for a different environment,
given by a family of independent simple symmetric random walks in equilibrium.

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The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
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The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
1
The categories of this paper are: cs