We consider finite collections of N non-intersecting Brownian paths on the line and on the half-line with both absorbing and reflecting boundary conditions (corresponding to Brownian excursions and reflected Brownian ...

We show that the squared maximal height of the top path amongNnon-intersecting Brownian bridges starting andending at the origin is distributed as the top eigenvalue of a random matrix drawn from the Laguerre Orthogonal ...

An explicit Fredholm determinant formula is derived for the multipoint distribution of the height function of the totally asymmetric simple exclusion process (TASEP) with arbitrary right-finite initial condition. The ...

We study the averaged product of characteristic polynomials of large random matrices in the Gaussian beta-ensemble perturbed by an external source of finite rank. We prove that at the edge of the spectrum, the limiting ...

This thesis explores the intersections between quantum computing, quantum physics and machine learning. In the three fields, estimating probability distributions plays a central role. In the case of quantum computing and ...