The distribution function for the maximal height of N non-intersecting Bessel paths

Abstract

In this paper, we consider N non-intersecting Bessel paths starting at \(x=a\ge 0\), and conditioned to end at the origin \(x=0\). We derive the explicit formula of the distribution function for the maximum height. Depending on the starting point \(a>0\) or \(a=0\), the distribution functions are also given in terms of the Hankel determinants associated with the multiple discrete orthogonal polynomials or discrete orthogonal polynomials, respectively.