Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Estimation of the last passage percolation constant in a charged
  complete directed acyclic graph via perfect simulation   Our object of study is the asymptotic growth of heaviest paths in a charged
(weighted with signed weights) complete directed acyclic graph. Edge charges
are i.i.d. random variables with common distribution $F$ supported on
$[-\infty,1]$ with essential supremum equal to $1$ (a charge of $-\infty$ is
understood as the absence of an edge). The asymptotic growth rate is a constant
that we denote by $C(F)$. Even in the simplest case where $F=p\delta_1 +
(1-p)\delta_{-\infty}$, corresponding to the longest path in the
Barak-Erd\H{o}s random graph, there is no closed-form expression for this
function, but good bounds do exist. In this paper we construct a Markovian
particle system that we call "Max Growth System" (MGS), and show how it is
related to the charged random graph. The MGS is a generalization of the
Infinite Bin Model that has been the object of study of a number of papers. We
then identify a random functional of the process that admits a stationary
version and whose expectation equals the unknown constant $C(F)$. Furthermore,
we construct an effective perfect simulation algorithm for this functional
which produces samples from the random functional.

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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
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The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph