Article
Survival asymptotics for branching random walks in IID environments Public Deposited
https://scholar.colorado.edu/concern/articles/nv935346t
- Abstract
- We first study a model, introduced recently in [4], of a critical branching random walk in an IID random environment on the d-dimensional integer lattice. The walker performs critical (0-2) branching at a lattice point if and only if there is no ‘obstacle’ placed there. The obstacles appear at each site with probability p ∈ [0, 1) independently of each other. We also consider a similar model, where the offspring distribution is subcritical. Let Sn be the event of survival up to time n. We show that on a set of full Ppmeasure, as n → ∞, P ω (Sn) ∼ 2/(qn) in the critical case, while this probability is asymptotically stretched exponential in the subcritical case. Hence, the model exhibits ‘self-averaging’ in the critical case but not in the subcritical one. I.e., in the first case, the asymptotic tail behavior is the same as in a ‘toy model’ where space is removed, while in the second, the spatial survival probability is larger than in the corresponding toy model, suggesting spatial strategies. A spine decomposition of the branching process along with known results on random walks are utilized.
- Creator
- Date Issued
- 2017-01-01
- Academic Affiliation
- Journal Title
- Journal Issue/Number
- 29
- Journal Volume
- 22
- File Extent
- 1-12
- Subject
- Last Modified
- 2019-12-05
- Resource Type
- Rights Statement
- DOI
- ISSN
- 1083-589X
- Language
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survivalAsymptoticsForBranchingRandomWalksInIidEnvironmen.pdf | 2019-12-05 | Public | Download | |
survivalAsymptoticsForBranchingRandomWalksInIidEnvironmen.pdf | 2019-12-05 | Public | Download |