Distances in the highly supercritical percolation cluster
  On the supercritical percolation cluster with parameter p, the distances between two distant points of the axis are asymptotically increased by a factor 1+(1-p)/2+o(1-p) with respect to the usual distance. The proof is based on an apparently new connection with the TASEP (totally asymmetric simple exclusion process). 
Anne-Laure Basdevant (MODAL'X), Nathana\"el Enriquez (MODAL'X, LPMA),   Lucas Gerin (MODAL'X)
math.PR