The hard-edge tacnode process for Brownian motion

Abstract

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 to the Aztec diamond on restricted domains.

35 pages, 2 figures

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Cited by in corpus (5)

• Extreme statistics of non-intersecting Brownian paths
• Fluctuations of the Arctic curve in the tilings of the Aztec diamond on restricted domains
• Double Interlacing in Random Tiling Models
• Nonintersecting Brownian bridges between reflecting or absorbing walls
• Scaling limit of domino tilings on a pentagonal domain