  We propose a matrix model which embodies the semiclassical approach to the
problem of quantum transport in chaotic systems. Specifically, a matrix
integral is presented whose perturbative expansion satisfies precisely the
semiclassical diagrammatic rules for the calculation of general counting
statistics. Evaluating it exactly, we show that it agrees with corresponding
predictions from random matrix theory. This uncovers the algebraic structure
behind the equivalence between these two approaches, and opens the way for
further semiclassical calculations.
