A Path Integral Approach to Age Dependent Branching Processes

Greenman, Christopher (2017) A Path Integral Approach to Age Dependent Branching Processes. Journal of Statistical Mechanics: Theory and Experiment, 2017 (March). ISSN 1742-5468

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Abstract

Age dependent population dynamics are frequently modeled with generalizations of the classic McKendrick-von Foerster equation. These are deterministic systems, and a stochastic generalization was recently reported in [1,2]. Here we develop a fully stochastic theory for age-structured populations via quantum field theoretical Doi-Peliti techniques. This results in a path integral formulation where birth and death events correspond to cubic and quadratic interaction terms. This formalism allows us to efficiently recapitulate the results in [1,2], exemplifying the utility of Doi-Peliti methods. Furthermore, we find that the path integral formulation for age-structured moments has an exact perturbative expansion that explicitly relates to the hereditary structure between correlated individuals. These methods are then generalized with a binary fission model of cell division.

Item Type: Article
Faculty \ School: Faculty of Science > School of Computing Sciences

University of East Anglia > Faculty of Science > Research Groups > Computational Biology (subgroups are shown below) > Analysis and models of genomic variation
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Depositing User: Pure Connector
Date Deposited: 22 Nov 2016 22:10
Last Modified: 22 Jul 2020 00:41
URI: https://ueaeprints.uea.ac.uk/id/eprint/61427
DOI: 10.1088/1742-5468/aa4f16

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