Analysis of Stochastic Chemical Reaction Networks with a Hierarchy of Timescales

IF 1.3 3区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
Lucie Laurence, Philippe Robert
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Abstract

We investigate a class of stochastic chemical reaction networks with \(n{\ge }1\) chemical species \(S_1\), ..., \(S_n\), and whose complexes are only of the form \(k_iS_i\), \(i{=}1\),..., n, where \((k_i)\) are integers. The time evolution of these CRNs is driven by the kinetics of the law of mass action. A scaling analysis is done when the rates of external arrivals of chemical species are proportional to a large scaling parameter N. A natural hierarchy of fast processes, a subset of the coordinates of \((X_i(t))\), is determined by the values of the mapping \(i{\mapsto }k_i\). We show that the scaled vector of coordinates i such that \(k_i{=}1\) and the scaled occupation measure of the other coordinates are converging in distribution to a deterministic limit as N gets large. The proof of this result is obtained by establishing a functional equation for the limiting points of the occupation measure, by an induction on the hierarchy of timescales and with relative entropy functions.

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来源期刊
Journal of Statistical Physics
Journal of Statistical Physics 物理-物理:数学物理
CiteScore
3.10
自引率
12.50%
发文量
152
审稿时长
3-6 weeks
期刊介绍: The Journal of Statistical Physics publishes original and invited review papers in all areas of statistical physics as well as in related fields concerned with collective phenomena in physical systems.
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