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CATEGORIES:Probability
SUMMARY:The contact process over a dynamical d-regular gra
ph - Daniel Valesin (Warwick)
DTSTART;TZID=Europe/London:20221122T153000
DTEND;TZID=Europe/London:20221122T163000
UID:TALK183200AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/183200
DESCRIPTION:We consider the contact process on a dynamic graph
defined as a random d-regular graph with a statio
nary edge-switching dynamics. In this graph dynami
cs\, independently of the contact process state\,
each pair {e1\,e2} of edges of the graph is replac
ed by new edges {e′1\,e′2} in a crossing fashion:
each of e′1\,e′2 contains one vertex of e1 and one
vertex of e2. As the number of vertices of the gr
aph is taken to infinity\, we scale the rate of sw
itching in a way that any fixed edge is involved i
n a switching with a rate that approaches a limiti
ng value v\, so that locally the switching is seen
in the same time scale as that of the contact pro
cess. We prove that if the infection rate of the c
ontact process is above a threshold value lambda_c
(depending on d and v)\, then the infection survi
ves for a time that grows exponentially with the s
ize of the graph. By proving that lambda_c is stri
ctly smaller than the lower critical infection rat
e of the contact process on the infinite d-regular
tree\, we show that there are values of lambda fo
r which the infection dies out in logarithmic time
in the static graph but survives exponentially lo
ng in the dynamic graph. Joint work with Gabriel L
eite Baptista da Silva and Roberto I. Oliveira.
LOCATION:MR12\, Centre for Mathematical Sciences
CONTACT:Perla Sousi
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