We consider a q-TASEP model started from step initial condition where all but finitely many particles have speed 1 and a few particles are slower. It is shown in Ferrari and Veto (2013) that the rescaled particles position of q-TASEP with identical hopping rates obeys a limit theorem à la...

We derive efficient recursive formulas giving the exact distribution of the largest eigenvalue for finite dimensional real Wishart matrices and for the Gaussian Orthogonal Ensemble (GOE). In comparing the exact distribution with the limiting distribution of large random matrices, we also found...