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

Nadine Guillotin-Plantard (1) , Yueyun Hu (2) , Bruno Schapira (3)

1 ICJ - Institut Camille Jordan
2 LAGA - Laboratoire Analyse, Géométrie et Applications
3 LATP - Laboratoire d'Analyse, Topologie, Probabilités

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 the 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.

Domaines: Probabilités [math.PR]

Nadine Guillotin-Plantard, Yueyun Hu, Bruno Schapira. The quenched limiting distributions of a one-dimensional random walk in random scenery.. Electronic Communications in Probability, 2013, 18 (85), pp.1-7. ⟨hal-00842602v2⟩