title: Exact distribution of the maximal height of p vicious walkers.
abstract: Using path-integral techniques, we compute exactly the distribution of the maximal height Hp of p nonintersecting Brownian walkers over a unit time interval in one dimension, both for excursions p watermelons with a wall, and bridges p watermelons without a wall, for all integer p>or=1. For large p, we show that <Hp> approximately square root 2p (excursions) whereas <Hp> approximately square root p (bridges). Our exact results prove that previous numerical experiments only measured the preasymptotic behaviors and not the correct asymptotic ones. In addition, our method establishes a physical connection between vicious walkers and random matrix theory.
authors.affiliation: Laboratoire de Physique Théorique (UMR du CNRS 8627), Université de Paris-Sud, 91405 Orsay Cedex, France.
authors.forename: Grégory
authors.initials: G
authors.lastname: Schehr
authors.forename: Satya N
authors.initials: SN
authors.lastname: Majumdar
authors.forename: Alain
authors.initials: A
authors.lastname: Comtet
authors.forename: Julien
authors.initials: J
authors.lastname: Randon-Furling