2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72471Let R_n be the radius of the largest disk covered after n steps of a simple random walk. We prove that almost surely limsup_{n \to \infty}(log R_n)^2/(log n log_3 n) = 1/4, where log_3 denotes 3 iterations of the log function. This is motivated by a question of Erdős and Taylor. We also obtain the analogous result for the Wiener sausage, refining a result of Meyre and Werner.18 pages to appear, Trans. Amer. Math. SocProbability60F15text