Abstract
Using path-integral techniques, we compute exactly the distribution of the maximal height of nonintersecting Brownian walkers over a unit time interval in one dimension, both for excursions watermelons with a wall, and bridges watermelons without a wall, for all integer . For large , we show that (excursions) whereas (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.
- Received 3 July 2008
DOI:https://doi.org/10.1103/PhysRevLett.101.150601
©2008 American Physical Society