Edge Universality for Nonintersecting Brownian Bridges

Abstract

In this paper we study fluctuations of extreme particles of nonintersecting Brownian bridges starting from $a_1\le a_2\le \cdots \le a_n$ at time $t=0$ and ending at $b_1\le b_2\le \cdots \le b_n$ at time $t=1$, where ${\mu }_{A_n}=(1/n){\sum }_i{\delta }_{a_i},{\mu }_{B_n}=(1/n){\sum }_i{\delta }_{b_i}$ are discretization of probability measures ${\mu }_A,{\mu }_B$. Under regularity assumptions of ${\mu }_A,{\mu }_B$, we show as the number of particles $n$ goes to infinity, fluctuations of extreme particles at any time $0<t<1$, after proper rescaling, are asymptotically universal, converging to the Airy point process.

arXiv comment56 pages, 4 figures. Draft version, comments are welcome

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