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arXiv · 1709.07141

The k-tacnode process

Robert Buckingham·Karl Liechty
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Abstract

The tacnode process is a universal behavior arising in nonintersecting particle systems and tiling problems. For Dyson Brownian bridges, the tacnode process describes the grazing collision of two packets of walkers. We consider such a Dyson sea on the unit circle with drift. For any integer k, we show that an appropriate double scaling of the drift and return time leads to a generalization of the tacnode process in which k particles are expected to wrap around the circle. We derive winding number probabilities and an expression for the correlation kernel in terms of functions related to the generalized Hastings-McLeod solutions to the inhomogeneous Painleve-II equation. The method of proof is asymptotic analysis of discrete orthogonal polynomials with a complex weight.

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Robert Buckingham, Karl Liechty. 2017-09-21. The k-tacnode process. https://arxiv.org/abs/1709.07141

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