An LIL for cover times of disks by planar random walk and Wiener sausage

• Autores: J. Ben Hough, Yuval Peres
• Localización: Transactions of the American Mathematical Society, ISSN 0002-9947, Vol. 359, Nº 10, 2007, págs. 4653-4668
• Idioma: inglés
• DOI: 10.1090/s0002-9947-07-03966-9
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• Resumen

  • Let be the radius of the largest disk covered after steps of a simple random walk. We prove that almost surely where denotes 3 iterations of the function. This is motivated by a question of Erdos and Taylor. We also obtain the analogous result for the Wiener sausage, refining a result of Meyre and Werner.