Dyson ’ s Nonintersecting Brownian Motions with a Few Outliers

  title={Dyson ’ s Nonintersecting Brownian Motions with a Few Outliers},
  author={Mark A Adler and JONATHAN DEL{\'E}PINE},
Consider n non-intersecting Brownian particles on R (Dyson Brownian motions), all starting from the origin at time t = 0, and forced to return to x = 0 at time t = 1. For large n, the average mean density of particles has its support, for each 0 < t < 1, on the interval ± √ 2nt(1− t). The Airy process A (τ) is defined as the motion of these non-intersecting Brownian motions for large n, but viewed from the curve C : y = √ 2nt(1− t) with an appropriate space-time rescaling. Assume now a finite… CONTINUE READING

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