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

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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.

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Authors and Affiliations

  1. Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong

    Dan Dai & Luming Yao

  2. School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Luming Yao

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  1. Dan Dai
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  2. Luming Yao
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Correspondence to Dan Dai.

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Dedicated to the memory of Richard Askey.

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This work was partially supported by grants from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 11300520), and by grants from City University of Hong Kong (Project Nos. 7005252, 7005597)

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Dai, D., Yao, L. The distribution function for the maximal height of N non-intersecting Bessel paths. Ramanujan J 61, 111–134 (2023). https://doi.org/10.1007/s11139-022-00567-3

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