Probability and Stochastic Analysis - University of Bonn

Abstract of "The hard-edge tacnode process for Brownian motion"

with Bálint Vető.

We consider N non-intersecting Brownian bridges conditioned to stay below a fixed threshold. We consider a scaling limit where the limit shape is tangential to the threshold. In the large N limit, we determine the limiting distribution of the top Brownian bridge conditioned to stay below a function as well as the limiting correlation kernel of the system. It is a one-parameter family of processes which depends on the tuning of the threshold position on the natural fluctuation scale. We also discuss the relation to the six-vertex model and the Aztec diamond on restricted domains.

Postscript file: [PS]

PDF file: [PDF]

arXiv: 1608.00394