title:Exceptional times for critical percolation under conservative dynamics
Abstract:
Start with an initial critical percolation configuration w_0 in the plane.
Let this configuration evolve in time according to a simple exclusion process
with kernel P(x,y)\sim |x-y|^{-2-\alpha}. In a joint work with Hugo
Vanneuville, we prove that if the long-range exponent \alpha is chosen
sufficiently small, then there exists “exceptional times” t for which an
infinite cluster appears in w_t. The existence of such exceptional times
for i.i.d dynamics (where sites evolve according to independent Poisson
Point process) goes back to the influential paper by Schramm-Steif in 2006.
Here, to handle such a conservative case, we push further the analysis of
“exclusion noise sensitivity” which had been initiated in Broman-Garban-Steif.