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SUMMARY:Scaling limit of an adaptive contact process - Daniel Valesin (Uni
versity of Warwick)
DTSTART;VALUE=DATE-TIME:20221128T120000Z
DTEND;VALUE=DATE-TIME:20221128T130000Z
UID:https://talks.ox.ac.uk/talks/id/7453685b-814a-429b-884d-3ce4f01ad20e/
DESCRIPTION:We introduce and study an interacting particle system evolving
on the d-dimensional torus \\Z^d_N. Each vertex of the torus can be eithe
r empty or occupied by an individual of a given type\; the space of all ty
pes is the positive real line. An individual of type \\lambda dies with ra
te one and gives birth at each neighbouring empty position with rate \\lam
bda. Moreover\, when the birth takes place\, the new individual is likely
to have the same type as the parent\, but has a small chance to be a mutan
t\; the mutation rate and law of the type of the mutant both depend on \\l
ambda. We consider the asymptotic behaviour of this process when the size
of the torus is taken to infinity and the overall rate of mutation tends t
o zero fast enough that mutations are sufficiently separated in time\, so
that the amount of time spent on configurations with more than one type be
comes negligible. We show that\, after a suitable projection (which extrac
ts just the dominant type from the configuration of individuals in the tor
us) and time scaling\, the process converges to a Markov jump process on t
he positive real lines\, whose rates we determine. Joint work with Adrián
González Casanova and András Tobias.\nSpeakers:\nDaniel Valesin (Univer
sity of Warwick)
LOCATION:Mathematical Institute (L5)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/7453685b-814a-429b-884d-3ce4f01ad20e/
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DESCRIPTION:Talk:Scaling limit of an adaptive contact process - Daniel Val
esin (University of Warwick)
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