Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strict comparison for the Lyapunov exponents of the simple random walk
  in random potentials   We consider the simple random walk in i.i.d. nonnegative potentials on the
$d$-dimensional cubic lattice $\mathbb{Z}^d$ ($d \geq 1$). In this model, the
so-called Lyapunov exponent describes the cost of traveling for the simple
random walk in the potential. The Lyapunov exponent depends on the distribution
function of the potential, and the aim of this article is to prove that the
Lyapunov exponent is strictly monotone in the distribution function of the
potential with the order according to strict dominance. In particular, for the
one-dimensional annealed situation, we observe that the Lyapunov exponents can
coincide even under the strict dominance. Furthermore, the comparison for the
Lyapunov exponent also provides that for the rate function of this model.

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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph