2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/17253The time-integrated current of the TASEP has non-Gaussian fluctuations of order $t^{1/3}$. The recently discovered connection to random matrices and the Painlevé II Riemann-Hilbert problem provides a technique through which we obtain the probability distribution of the current fluctuations, in particular their dependence on initial conditions, and the stationary two-point function. Some open problems are explained.19 pages, 4 figures, the correct 2x2 distribution for the semi-infinite case has been includedStatistical MechanicsProbabilitytext