Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Remarks on random walks on graphs and the Floyd boundary   We show that for a uniformly irreducible random walk on a graph, with bounded
range, there is a Floyd function for which the random walk converges to its
corresponding Floyd boundary. Moreover if we add the assumptions,
$p^{(n)}(v,w)\leq C \rho^n$, where $\rho < 1$ is the spectral radius, then for
any Floyd function $f$ that satisfies $\sum_{n=1}^{\infty}nf(n)<\infty$, the
Dirichlet problem with respect to the Floyd boundary is solvable.

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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
1
The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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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: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: nlin