On multidimensional branching random walks in random environment

DOI10.1214/009117906000000926zbMath1114.60084arXivmath/0507126OpenAlexW2949169981MaRDI QIDQ879249

Francis Comets, Serguei Popov

Publication date: 8 May 2007

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0507126

Mathematics Subject Classification ID

Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) (82D30) Processes in random environments (60K37) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (18)

Spread of a catalytic branching random walk on a multidimensional lattice ⋮ Minimal position of branching random walks in random environment ⋮ Large and moderate deviations for a -valued branching random walk with a random environment in time ⋮ Quenched invariance principles for the maximal particle in branching random walk in random environment and the parabolic Anderson model ⋮ Survival of branching random walks in random environment ⋮ Competition on \(\mathbb{Z}^d\) driven by branching random walk ⋮ Extinction probabilities in branching processes with countably many types: a general framework ⋮ On the trace of branching random walks ⋮ Asymptotic shape for the contact process in random environment ⋮ Ancestral lineages and limit theorems for branching Markov chains in varying environment ⋮ A pathwise approach to the extinction of branching processes with countably many types ⋮ The speed of a branching system of random walks in random environment ⋮ Branching random walks with random environments in time ⋮ Unnamed Item ⋮ Intermittency for branching random walk in Pareto environment ⋮ Exact convergence rates in central limit theorems for a branching random walk with a random environment in time ⋮ Subsequential tightness for branching random walk in random environment ⋮ Exact convergence rate of the local limit theorem for a branching random walk in a time-dependent random environment on d-dimensional integer lattice

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Tail estimates for one-dimensional random walk in random environment
• A discrete stochastic integral inequality and balanced random walk in a random environment
• An improved subadditive ergodic theorem
• Branching random walk in random environment phase transitions for local and global growth rates
• Subadditive ergodic theory
• Quenched sub-exponential tail estimates for one-dimensional random walk in random environment
• Precise large deviation estimates for a one-dimensional random walk in a random environment
• Lyapounov exponents and quenched large diviations for multidimensional random walk in random environment
• A note on transience versus recurrence for a branching random walk in random environment
• Large deviation principle for random walk in a quenched random environment in the flow speed regime
• Slowdown estimates and central limit theorem for random walks in random environment
• A law of large numbers for random walks in random environment
• An effective criterion for ballistic behavior of random walks in random environment
• A non-ballistic law of large numbers for random walks in i. i. d. random environment
• On new examples of ballistic random walks in random environment
• The shape theorem for the frog model
• Slowdown and neutral pockets for a random walk in random environment
• A variational approach to branching random walk in random environment
• The speed of a branching system of random walks in random environment
• Branching random walk in random environment on trees.
• One-dimensional branching random walks in a Markovian random environment
• On the Williams-Bjerknes tumour growth model: II
• Contact processes in several dimensions
• The asymptotic shape of the branching random walk
• Large deviations for random walks in a random environment
• Topics in the Constructive Theory of Countable Markov Chains
• Large deviations of sums of independent random variables

This page was built for publication: On multidimensional branching random walks in random environment