Convex Hulls of Random Walks: Large-Deviation Properties

Gunnar Claussen ¹ Alexander K. Hartmann ¹ Satya N. Majumdar ²

Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2015, 91, pp.052104

We study the convex hull of the set of points visited by a two-dimensional random walker of T discrete time steps. Two natural observables that characterize the convex hull in two dimensions are its perimeter L and area A. While the mean perimeter

• 1. Institut für Physik
• 2. LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques