Localized growth and branching random walks with time correlations

Localized growth and branching random walks with time correlations.

We generalize a model of growth over a disordered environment, to a large class of Itō processes. In particular, we study how the microscopic properties of the noise influence the macroscopic growth rate. The present model can account for growth processes in large dimensions and provides a bed to understand better the tradeoff between exploration and exploitation. An additional mapping to the S...

Branching Random Walks in Time Inhomogeneous Environments

We study the maximal displacement of branching random walks in a class of time inhomogeneous environments. Specifically, binary branching random walks with Gaussian increments will be considered, where the variances of the increments change over time macroscopically. We find the asymptotics of the maximum up to an OP (1) (stochastically bounded) error, and focus on the following phenomena: the ...

Branching Random Walks in Space-Time Random Environment: Survival Probability, Global and Local Growth Rates

We study the survival probability and the growth rate for branching random walks in random environment (BRWRE). The particles perform simple symmetric random walks on the d-dimensional integer lattice, while at each time unit, they split into independent copies according to time-space i.i.d. offspring distributions. The BRWRE is naturally associated with the directed polymers in random environm...

Branching Random Walks

We study a generalized branching random walk where particles breed at a rate which depends on the number of neighbouring particles. Under general assumptions on the breeding rates we prove the existence of a phase where the population survives without exploding. We construct a non trivial invariant measure for this case.

Branching Processes and Random Walks