Wiener sausages

a a For a 0, let W1 (t) and W2 (t) be the a-neighbourhoods of two independent standard Brownian motions in Rd starting at 0 and observed until time t. We prove that, for d ≥ 3 and c 0, t→∞ t(d−2)/d lim 1 κ a a log P |W1 (ct) ∩ W2 (ct)| ≥ t = −Id a (c) κ and derive a variational representation for the rate constant Id a (c). Here, κa is the Newtonian capacity of the ball with radius a. We show that the optimal a a strategy to realise the above large deviation is for...

44p tuanloccuoi 04-01-2013 51 7   Download