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SUMMARY:Alexander Stauffer (University of Bath)
DTSTART:20221116T140000Z
DTEND:20221116T150000Z
DTSTAMP:20260423T021038Z
UID:ADPS/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ADPS/9/">Non
 -equilibrium multi-scale analysis and coexistence in competing first-passa
 ge percolation</a>\nby Alexander Stauffer (University of Bath) as part of 
 Abu Dhabi Stochastics Seminar\n\n\nAbstract\nWe consider a natural random 
 growth process with competition on Z^d called first-passage percolation in
  a hostile environment\, that consists of two first-passage percolation pr
 ocesses FPP_1 and FPP_\\lambda that compete for the occupancy of sites. In
 itially FPP_1 occupies the origin and spreads through the edges of Z^d at 
 rate 1\, while FPP_\\lambda is initialised at sites called seeds that are 
 distributed according to a product of Bernoulli measures of parameter p. A
  seed remains dormant until FPP_1 or FPP_\\lambda attempts to occupy it\, 
 after which it spreads through the edges of Z^d at rate \\lambda. We will 
 discuss the results known for this model and present a recent proof that t
 he two types can coexist (concurrently produce an infinite cluster) on Z^d
 . We remark that\, though counterintuitive\, the above model is not monoto
 ne in the sense that adding a seed of FPP_\\lambda could favor FPP_1. A ce
 ntral contribution of our work is the development of a novel multi-scale a
 nalysis to analyze this model\, which we call a multi-scale analysis with 
 non-equilibrium feedback and which we believe could help analyze other mod
 els with non-equilibrium dynamics and lack of monotonicity. Based on joint
  works with Vladas Sidoravicius and Tom Finn.\n
LOCATION:https://researchseminars.org/talk/ADPS/9/
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