Random walks and branching processes in correlated Gaussian environment
arXiv:1607.00999 · doi:10.1007/s10955-016-1677-7
Abstract
We study persistence probabilities for random walks in correlated Gaussian random environment first studied by Oshanin, Rosso and Schehr. From the persistence results, we can deduce properties of critical branching processes with offspring sizes geometrically distributed with correlated random parameters. More precisely, we obtain estimates on the tail distribution of its total population size, of its maximum population, and of its extinction time.
References in corpus (9)
- Persistence and First-Passage Properties in Non-equilibrium Systems
- Random Walkers in 1-D Random Environments: Exact Renormalization Group Analysis
- Persistence in Nonequilibrium Systems
- Hitting probability for anomalous diffusion processes
- Anomalous fluctuations of currents in Sinai-type random chains with strongly correlated disorder
- Diffusion in periodic, correlated random forcing landscapes
- Persistence probabilities \& exponents
- Persistence of fractional Brownian motion with moving boundaries and applications
- Asymptotic of the distribution and harmonic moments for a supercritical branching process in a random environment