zbMATH — the first resource for mathematics

Asymptotic estimation of the radius of the largest disc covered by the planar Wiener sausage. (Estimation asymptotique du rayon du plus grand disque recouvert par la saucisse de Wiener plane.) (French) Zbl 0828.60066
Summary: Let \(S_t\) be the Wiener sausage of radius 1 associated with a planar Brownian motion started at 0, on the time-interval \([0,t]\). Denote by \(R(t)\) the radius of the largest disc centered at the origin covered by \(S_t\). We obtain asymptotic results for \(R(t)\) as \(t \to \infty\). In particular, we prove the existence of \(c \in [1/8,1]\) so that almost surely, \(\lim \sup_{t \to \infty} (\log R(t))^2/(\log t \log_3t) = c\).

60J65 Brownian motion
Full Text: DOI