Dormancy in random environment: Symmetric exclusion
Authors
- Shafigh, Helia
ORCID: 0009-0003-8160-9204
2020 Mathematics Subject Classification
- 60J28 60K35 92D25
Keywords
- Parabolic Anderson model, dormancy, populations with seed-bank, branching random walk, Lyapunov exponents, Rayleigh--Ritz formula, switching diffusions, Feynman--Kac formula, simple symmetric exclusion process
DOI
Abstract
In this paper, we study a spatial model for dormancy in random environment via a two-type branching random walk in continuous-time, where individuals can switch between dormant and active states through spontaneous switching independent of the random environment. However, the branching mechanism is governed by a random environment which dictates the branching rates, namely the simple symmetric exclusion process. We will interpret the presence of the exclusion particles either as emphcatalysts, accelerating the branching mechanism, or as emphtraps, aiming to kill the individuals. The difference between active and dormant individuals is defined in such a way that dormant individuals are protected from being trapped, but do not participate in migration or branching. We quantify the influence of dormancy on the growth resp. survival of the population by identifying the large-time asymptotics of the expected population size. The starting point for our mathematical considerations and proofs is the parabolic Anderson model via the Feynman-Kac formula. In particular, the quantitative investigation of the role of dormancy is done by extending the Parabolic Anderson model to a two-type random walk
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