Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The zero-one law for planar random walks in i.i.d. random environments
  revisited   In this note we present a simplified proof of the zero-one law by Merkl and
Zerner (2001) for directional transience of random walks in i.i.d. random
environments (RWRE) on the square lattice. Also, we indicate how to construct a
two-dimensional counterexample in a non-uniformly elliptic and stationary
environment which has better ergodic properties than the example given by Merkl
and Zerner.

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The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
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The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
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The categories of this paper are: econ
7
The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con