Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hitting times of Bessel processes, volume of Wiener sausages and zeros
  of Macdonald functions   We derive formulae for some ratios of the Macdonald functions, which are
simpler and easier to treat than known formulae. The result gives two
applications in probability theory. One is the formula for the L{\'e}vy measure
of the distribution of the first hitting time of a Bessel process and the other
is an explicit form for the expected volume of the Wiener sausage for an even
dimensional Brownian motion. Moreover, the result enables us to write down the
algebraic equations whose roots are the zeros of Macdonald functions.

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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
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The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc