Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mean-field equation for a stochastic many-particle model of
  quorum-sensing microbial populations   We prove a mean-field equation for the dynamics of quorum-sensing microbial
populations. In the stochastic many-particle process, individuals of a
population produce public good molecules to different degrees. Individual
production is metabolically costly such that non-producers replicate faster
than producers. In addition, individuals sense the average production level in
the well-mixed population and adjust their production in response ("quorum
sensing"). Here we prove that the temporal evolution of such quorum-sensing
populations converges to a macroscopic mean-field equation for increasing
population sizes. To prove convergence, we introduce an auxiliary stochastic
mean-field process that mimics the dynamics of the mean-field equation and that
samples independently the individual's production degrees between consecutive
update steps. This way, the law of large numbers is separated from the
propagation of errors due to correlations. Our developed method of an auxiliary
stochastic mean-field process may help to prove mean-field equations for other
stochastic many-particle processes.

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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-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: eess