%0 Journal Article %1 birkner2016random %A Birkner, Matthias %A Černý, Jiří %A Depperschmidt, Andrej %D 2016 %I Institute of Mathematical Statistics %J Electronic Journal of Probability %K ancestry_tracing lineage_movement percolation %N none %R 10.1214/16-ejp4666 %T Random walks in dynamic random environments and ancestry under local population regulation %U https://doi.org/10.1214%2F16-ejp4666 %V 21 %X 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.

@article{birkner2016random, 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.}, added-at = {2021-06-30T17:49:11.000+0200}, author = {Birkner, Matthias and Černý, Jiří and Depperschmidt, Andrej}, biburl = {https://www.bibsonomy.org/bibtex/2f2fc57c74fb465540717453f6b8f017d/peter.ralph}, doi = {10.1214/16-ejp4666}, interhash = {ba6b4cb3e1d8d3029d2100fc8dc13e06}, intrahash = {f2fc57c74fb465540717453f6b8f017d}, journal = {Electronic Journal of Probability}, keywords = {ancestry_tracing lineage_movement percolation}, month = jan, number = {none}, publisher = {Institute of Mathematical Statistics}, timestamp = {2021-06-30T17:49:11.000+0200}, title = {Random walks in dynamic random environments and ancestry under local population regulation}, url = {https://doi.org/10.1214%2F16-ejp4666}, volume = 21, year = 2016 }