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math-ph2019
The distribution function for the maximal height of non-intersecting Bessel paths
Dan Dai, Luming Yao
In this paper, we consider non-intersecting Bessel paths starting at , and conditioned to end at the origin . We derive the explicit formula of the distribution…
math-ph2019
On integrals of the tronquée solutions and the associated Hamiltonians for the Painlevé II equation
Dan Dai, Shuai-Xia Xu, Lun Zhang
We consider a family of tronquée solutions of the Painelvé II equation \begin{equation*} q''(s)=2q(s)^3+sq(s)-(2α+\frac12), \qquad α> -\frac12, \end{equation*} which is characteriz…