作者：Baik, Jinho; Barraquand, Guillaume; Corwin, Ivan; Suidan, Toufic
作者单位：University of Michigan System; University of Michigan; Columbia University
摘要：We study last passage percolation in a half-quadrant, which we analyze within the framework of Pfaffian Schur processes. For the model with exponential weights, we prove that the fluctuations of the last passage time to a point on the diagonal are either GSE Tracy-Widom distributed, GOE Tracy- Widom distributed or Gaussian, depending on the size of weights along the diagonal. Away from the diagonal, the fluctuations of passage times follow the GUE Tracy-Widom distribution. We also obtain a two...
作者：Denisov, Denis; Sakhanenko, Alexander; Wachtel, Vitali
作者单位：University of Manchester; Nankai University; University of Augsburg
摘要：We consider random walks with independent but not necessarily identical distributed increments. Assuming that the increments satisfy the well-known Lindeberg condition, we investigate the asymptotic behaviour of first passage times over moving boundaries. Furthermore, we prove that a properly rescaled random walk conditioned to stay above the boundary up to time n converges, as n -> infinity towards the Brownian meander.
