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December 2015 Scaling limits of spatial compartment models for chemical reaction networks
Peter Pfaffelhuber, Lea Popovic
Ann. Appl. Probab. 25(6): 3162-3208 (December 2015). DOI: 10.1214/14-AAP1070


We study the effects of fast spatial movement of molecules on the dynamics of chemical species in a spatially heterogeneous chemical reaction network using a compartment model. The reaction networks we consider are either single- or multi-scale. When reaction dynamics is on a single-scale, fast spatial movement has a simple effect of averaging reactions over the distribution of all the species. When reaction dynamics is on multiple scales, we show that spatial movement of molecules has different effects depending on whether the movement of each type of species is faster or slower than the effective reaction dynamics on this molecular type. We obtain results for both when the system is without and with conserved quantities, which are linear combinations of species evolving only on the slower time scale.


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Peter Pfaffelhuber. Lea Popovic. "Scaling limits of spatial compartment models for chemical reaction networks." Ann. Appl. Probab. 25 (6) 3162 - 3208, December 2015.


Received: 1 February 2013; Revised: 1 July 2014; Published: December 2015
First available in Project Euclid: 1 October 2015

zbMATH: 1329.60341
MathSciNet: MR3404634
Digital Object Identifier: 10.1214/14-AAP1070

Primary: 60J25, 60J27
Secondary: 60F17, 80A30, 92C45

Rights: Copyright © 2015 Institute of Mathematical Statistics


Vol.25 • No. 6 • December 2015
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