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SUMMARY:On the contact process in an evolving random environment - Anja St
urm (University of Göttingen)
DTSTART;VALUE=DATE-TIME:20220516T120000
DTEND;VALUE=DATE-TIME:20220516T130000
UID:https://talks.ox.ac.uk/talks/id/39ad6c9f-1581-4058-8633-336d40058330/
DESCRIPTION:Recently\, there has been increasing interest in interacting p
article systems on evolving random graphs\, respectively in time evolving
random environments. In this talk we will present some results on the cont
act process in a evolving (edge) random environment on (infinite) connecte
d and transitive graphs with bounded degrees. We assume that the evolving
random environment is described by an autonomous ergodic spin systems with
finite range\, for example by dynamical percolation. This background proc
ess determines which edges are open or closed for infections.\n\nMost cont
ribution to this class of models are very recent and we will give a short
overview. Our own resulsts concern the dependence of the critical infectio
n rate for survival on the random environment and on the initial configura
tion of the system. For the latter we state sufficient conditions such tha
t the initial configuration of the system has no influence on the phase tr
ansition between extinction and survival. We show that this phase transiti
on coincides with the phase transition between a trivial/non-trivial uppe
r invariant law. We also discuss the continuity properties of the surviva
l probability as well as conditions for complete convergence.\nFinally\, w
e touch upon considering the contact process on dynamical long range perc
olation and discuss some open problems\, conjecture and further research d
irections.\n\nThis is joint work with Marco Seiler (University of Götting
en).\n\nSpeakers:\nAnja Sturm (University of Göttingen)
LOCATION:Mathematical Institute (Lecture Room 4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/39ad6c9f-1581-4058-8633-336d40058330/
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DESCRIPTION:Talk:On the contact process in an evolving random environment
- Anja Sturm (University of Göttingen)
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