Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact distribution of the maximal height of p vicious walkers   Using path integral techniques, we compute exactly the distribution of the
maximal height H_p 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\ge 1. For large p, we
show that < H_p > \sim \sqrt{2p} (excursions) whereas < H_p > \sim \sqrt{p}
(bridges). Our exact results prove that previous numerical experiments only
measured the pre-asymptotic behaviors and not the correct asymptotic ones. In
addition, our method establishes a physical connection between vicious walkers
and random matrix theory.

35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph