Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Beyond Hammersley's Last-Passage Percolation: a discussion on possible
  local and global constraints   Hammersley's Last-Passage Percolation (LPP), also known as Ulam's problem, is
a well-studied model that can be described as follows: consider $m$ points
chosen uniformly and independently in $[0,1]^2$, then what is the maximal
number $\mathcal{L}_m$ of points that can be collected by an up-right path? We
introduce here a generalization of this standard LPP, in order to allow for
more general constraints than the up-right condition (a $1$-Lipschitz condition
after rotation by $45^{\circ}$). We focus more specifically on two cases: (i)
when the constraint is a $\gamma$-H\"older (local) condition, we call it H-LPP;
(ii) when the constraint is a path-entropy (global) condition, we call it
E-LPP. These generalizations also allows us to deal with non-directed LPP. We
develop motivations for directed and non-directed constrained LPP, and we give
the correct order of $\mathcal{L}_m$ in a general manner.

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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: cs
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an