How can a clairvoyant particle escape the exclusion process?

Rangel Baldasso, Augusto Teixeira

Published 2016-05-24Version 1

We study a detection problem in the following setting: on the integer lattice, at time zero, place nodes on each site independently with probability $\rho \in [0,1)$ and let them evolve as an exclusion process. At time zero, place a target at the origin. The target moves only at integer times, and can move to any site that is within distance R from its current position. Assume also that the target can predict the future movement of all nodes. We prove that, for R large enough (depending on the value of $\rho$) it is possible for the target to avoid detection forever with positive probability. The proof of this result uses two ingredients of independent interest. First we establish a renormalisation scheme that can be used to prove percolation for dependent oriented models under a certain decoupling condition. The second step of the proof is a space-time decoupling for the exclusion process.