Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The generating function of the survival probabilities in a cone is not
  rational   A. We look at multidimensional random walks (Sn) n 0 in convex cones, and
address the question of whether two naturally associated generating functions
may define rational functions. The first series is the one of the survival
probabilities P($\tau$ > n), where $\tau$ is the first exit time from a given
cone; the second series is that of the excursion probabilities P($\tau$ > n, Sn
= y). Our motivation to consider this question is twofold: first, it goes along
with a global effort of the combinatorial community to classify the algebraic
nature of the series counting random walks in cones; second, rationality
questions of the generating functions are strongly associated with the
asymptotic behaviors of the above probabilities, which have their own interest.
Using wellknown relations between rationality of a series and possible
asymptotics of its coefficients, recent probabilistic estimates immediately
imply that the excursion generating function is not rational. Regarding the
survival probabilities generating function, we propose a short, elementary and
selfcontained proof that it cannot be rational neither.

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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con