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.