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2016 Random walks in dynamic random environments and ancestry under local population regulation
Matthias Birkner, Jiří Černý, Andrej Depperschmidt
Electron. J. Probab. 21: 1-43 (2016). DOI: 10.1214/16-EJP4666

Abstract

We consider random walks in dynamic random environments, with an environment generated by the time-reversal of a Markov process from the oriented percolation universality class. If the influence of the random medium on the walk is small in space-time regions where the medium is typical, we obtain a law of large numbers and an averaged central limit theorem for the walk via a regeneration construction under suitable coarse-graining.

Such random walks occur naturally as spatial embeddings of ancestral lineages in spatial population models with local regulation. We verify that our assumptions hold for logistic branching random walks when the population density is sufficiently high.

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Matthias Birkner. Jiří Černý. Andrej Depperschmidt. "Random walks in dynamic random environments and ancestry under local population regulation." Electron. J. Probab. 21 1 - 43, 2016. https://doi.org/10.1214/16-EJP4666

Information

Received: 27 October 2015; Accepted: 23 April 2016; Published: 2016
First available in Project Euclid: 26 May 2016

zbMATH: 1345.60120
MathSciNet: MR3508685
Digital Object Identifier: 10.1214/16-EJP4666

Subjects:
Primary: 60J10, 60K35, 60K37, 82B43

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