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

## TL;DR

This paper derives explicit formulas for the distribution of the maximum height of N non-intersecting Bessel paths starting at a point and ending at zero, using orthogonal polynomial techniques.

## Contribution

It provides new explicit formulas for the maximum height distribution of non-intersecting Bessel paths, linking it to Hankel determinants and orthogonal polynomials.

## Key findings

- Distribution functions expressed via Hankel determinants.
- Formulas depend on initial starting point a.
- Results applicable to non-intersecting Bessel path models.

## Abstract

In this paper, we consider $N$ non-intersecting Bessel paths starting at $x=a\geq 0$, 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.