Stretched Exponential Decay For Subcritical Parking Times On Double-Struck Capital Zd

At each vertex of DOUBLE-STRUCK CAPITAL Zd, place a car with probability p or vacant parking spot with probability 1 - p. Cars perform independent random walks and park at vacant spots, rendering them passable. There is a transition at p = 1/2: the origin is a.s. visited by finitely many distinct cars when p < 1/2, and by infinitely many when p >= 1/2. Furthermore, a.s. all cars park if p <= 1/2 and some never park for p > 1/2. For small p, we prove that the parking time tau of the car initially at the origin satisfies exp those previously obtained in the case of moving obstacles.