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- W4284962013 abstract "We introduce and study an interacting particle system evolving on the $d$-dimensional torus $(mathbb Z/Nmathbb Z)^d$. Each vertex of the torus can be either empty or occupied by an individual of type $lambda in (0,infty)$. An individual of type $lambda$ dies with rate one and gives birth at each neighboring empty position with rate $lambda$; moreover, when the birth takes place, the newborn individual is likely to have the same type as the parent, but has a small probability of being a mutant. A mutant child of an individual of type $lambda$ has type chosen according to a probability kernel. We consider the asymptotic behavior of this process when $Nto infty$ and the parameter $delta_N$ tends to zero fast enough that mutations are sufficiently separated in time, so that the amount of time spent on configurations with more than one type becomes negligible. We show that, after a suitable time scaling and deletion of the periods of time spent on configurations with more than one type, the process converges to a Markov jump process on $(0,infty)$, whose rates we characterize." @default.
- W4284962013 created "2022-07-10" @default.
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- W4284962013 date "2022-07-07" @default.
- W4284962013 modified "2023-10-09" @default.
- W4284962013 title "Scaling limit of an adaptive contact process" @default.
- W4284962013 doi "https://doi.org/10.48550/arxiv.2207.03455" @default.
- W4284962013 hasPublicationYear "2022" @default.
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