Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Longest increasing paths with gaps   We consider a variant of the continuous and discrete Ulam-Hammersley
problems: we study the maximal length of an increasing path through a Poisson
point process (or a Bernoulli point process) with the restriction that there
must be minimal gaps between abscissae and ordinates of successive points of
the path.For both cases (continuous and discrete) our approach rely on
couplings with well-studied models: respectively the classical Ulam-Hammersley
problem and last-passage percolation with geometric weights. Thanks to these
couplings we obtain explicit limiting shapes in both settings.We also establish
that, as in the classical Ulam-Hammersley problem, the fluctuations around the
mean are given by the Tracy-Widom distribution.

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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: cs
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The categories of this paper are: supr-con
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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: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio