The hard edge tacnode process and the hard edge Pearcey process with nonintersecting squared Bessel paths
Abstract
A system of nonintersecting squared Bessel processes is considered which all start from one point and they all return to another point. Under the scaling of the starting and ending points when the macroscopic boundary of the paths touches the hard edge, a limiting critical process is described in the neighbourhood of the touching point which we call the hard edge tacnode process. We derive its correlation kernel in an explicit new form which involves Airy type functions and operators that act on the direct sum of $L^2(\mathbb R_+)$ and a finite dimensional space. As the starting points of the squared Bessel paths are set to 0, a cusp in the boundary appears. The limiting process is described near the cusp and it is called the hard edge Pearcey process. We compute its multitime correlation kernel which extends the existing formulas for the singletime kernel. Our preasymptotic correlation kernel involves the ratio of two Toeplitz determinants which are rewritten using a BorodinOkounkov type formula.
 Publication:

arXiv eprints
 Pub Date:
 December 2014
 arXiv:
 arXiv:1412.0831
 Bibcode:
 2014arXiv1412.0831D
 Keywords:

 Mathematics  Probability;
 60K35;
 60B20
 EPrint:
 49 pages, 4 figures