Clusters of a Random Walk on the Plane

Revesz, P.

Ann. Probab., Tome 21 (1993) no. 4, p. 318-328 / Harvested from Project Euclid

Résumé

Let $r(n)$ be the radius of the largest disc covered by $S(1),\ldots, S(n)$, where $\{S(k); k = 1, 2,\ldots\}$ is the simple symmetric random walk on $Z^2$. The main result tells us that $r(n) \geq n^{1/50}$ a.s. for all but finitely many $n$.

Détail

Publié le : 1993-01-14
Classification:  Random walk on the plane,  covered discs,  strong laws,  local time,  60F15,  60J55