The height and range of watermelons without wall

Abstract

We determine the weak limit of the distribution of the random variables "height" and "range" on the set of p-watermelons without wall restriction as the number of steps tends to infinity. Additionally, we provide asymptotics for the moments of the random variable "height".

13 pages and 2 figures. More detailed representation. Improved Theorem 2 (height moment asymptotics)

References in corpus (3)

• Maximum distributions of bridges of noncolliding Brownian paths
• Vicious Random Walkers and a Discretization of Gaussian Random Matrix Ensembles
• Functional central limit theorems for vicious walkers

Cited by in corpus (3)

• Airy processes and variational problems
• Distribution of the time at which N vicious walkers reach their maximal height
• Non-intersecting Brownian bridges and the Laguerre Orthogonal Ensemble