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SUMMARY:The contact process over a dynamical d-regular graph - Daniel Vale
 sin (Warwick)
DTSTART:20221122T153000Z
DTEND:20221122T163000Z
UID:TALK183200@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:We consider the contact process on a dynamic graph defined as 
 a random d-regular graph with a stationary edge-switching dynamics. In thi
 s graph dynamics\, independently of the contact process state\, each pair 
 {e1\,e2} of edges of the graph is replaced 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 graph is taken to infinity
 \, we scale the rate of switching in a way that any fixed edge is involved
  in a switching with a rate that approaches a limiting value v\, so that l
 ocally the switching is seen in the same time scale as that of the contact
  process. We prove that if the infection rate of the contact process is ab
 ove a threshold value lambda_c (depending on d and v)\, then the infection
  survives for a time that grows exponentially with the size of the graph. 
 By proving that lambda_c is strictly smaller than the lower critical infec
 tion rate of the contact process on the infinite d-regular tree\, we show 
 that there are values of lambda for which the infection dies out in logari
 thmic time in the static graph but survives exponentially long in the dyna
 mic graph. Joint work with Gabriel Leite Baptista da Silva and Roberto I. 
 Oliveira.
LOCATION:MR12\, Centre for Mathematical Sciences
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