The quenched limiting distributions of a one-dimensional random walk in random scenery

Nadine Guillotin-Plantard (Université Lyon 1)
Yueyun Hu (Université Paris 13)
Bruno Schapira (Aix-Marseille Université)


For a one-dimensional random walk in random scenery (RWRS) on Z, we determine its quenched weak limits by applying Strassen's functional law of iterated logarithm. As a consequence, conditioned on the random scenery, the one dimensional RWRS does not converge in law, in contrast with the multi-dimensional case.

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Pages: 1-7

Publication Date: November 3, 2013

DOI: 10.1214/ECP.v18-2918


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