Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local time for lattice paths and the associated limit laws   For generalized Dyck paths (i.e., directed lattice paths with any finite set
of jumps), we analyse their local time at zero (i.e., the number of times the
path is touching or crossing the abscissa). As we are in a discrete setting,
the event we analyse here is '' invisible '' to the tools of Brownian motion
theory. It is interesting that the key tool for analysing directed lattice
paths, which is the kernel method, is not directly applicable here. Therefore,
we introduce a variant of this kernel method to get the trivariate generating
function (length, final altitude, local time): this leads to an expression
involving symmetric and algebraic functions. We apply this analysis to
different types of constrained lattice paths (meanders , excursions, bridges,.
. .). Then, we illustrate this approach on 'basketball walks ' which are walks
defined by the jumps --2, --1, 0, +1, +2. We use singularity analysis to prove
that the limit laws for the local time are (depending on the drift and the type
of walk) the geometric distribution, the negative binomial distribution, the
Rayleigh distribution, or the half-normal distribution (a universal
distribution up to now rarely encountered in analytic combinatorics).

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The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org