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RESEARCH PRODUCT
Random walks in dynamic random environments and ancestry under local population regulation
Matthias BirknerJiří ČErnýAndrej Depperschmidtsubject
Statistics and Probability82B43Markov processRandom walklogistic branching random walk01 natural sciences60K37 60J10 60K35 82B43010104 statistics & probabilitysymbols.namesakeMathematics::ProbabilityFOS: MathematicsLocal populationStatistical physics0101 mathematicsoriented percolationCentral limit theoremMathematicsdynamical random environmentProbability (math.PR)010102 general mathematicsRandom mediaRenormalization groupsupercritical clusterRandom walk60K37Population model60K35central limit theorem in random environmentPercolationsymbols60J10Statistics Probability and UncertaintyMathematics - Probabilitydescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-05-11 | Electronic Journal of Probability |