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Upper limits of Sinai’s walk in random scenery

2007; Elsevier BV; Volume: 118; Issue: 6 Linguagem: Inglês

10.1016/j.spa.2007.07.006

1879-209X

Olivier Zindy,

Point processes and geometric inequalities

We consider Sinai’s walk in i.i.d. random scenery and focus our attention on a conjecture of Révész concerning the upper limits of Sinai’s walk in random scenery when the scenery is bounded from above. A close study of the competition between the concentration property for Sinai’s walk and negative values for the scenery enables us to prove that the conjecture is true if the scenery has “thin” negative tails and is false otherwise.