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.
Users
Please
log in to take part in the discussion (add own reviews or comments).