Stationary activated random walk: regularity, heavy tails, and remixing

Source abstract

We study the stationary state of driven-dissipative activated random walk on an interval of length $n$ and prove that subintervals down to size $\log n$ have particle density near the critical value. We then deduce that the avalanche area is heavy-tailed and that the process forgets an initial stationary state after $o(n)$ steps. We conjecture that the density fluctuations, avalanche area, and remixing time from stationarity are governed by the same critical exponent.