Boundary of the Range II: Lower Tails

Amine Asselah (1) , Bruno Schapira (2)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 I2M - Institut de Mathématiques de Marseille

We study downward deviations of the boundary of the range of a transient walk on the Euclidean lattice. We describe the optimal strategy adopted by the walk in order to shrink the boundary of its range. The technics we develop apply equally well to the range, and provide pathwise statements for the Swiss cheese picture of Bolthausen, van den Berg and den Hollander [BBH01].

Mots clés: Large deviations; boundary of the range; capacity.

Domaines: Probabilités [math.PR]

Amine Asselah, Bruno Schapira. Boundary of the Range II: Lower Tails. 2016. ⟨hal-01257015v1⟩