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We study the cumulants and their generating functions of the probabilitydistributions of the conductance, shot noise and Wigner delay time in ballisticquantum dots. Our approach is based on the integrable theory of certain matrixintegrals and applies to all the symmetry classes beta=1,2,4 of Random MatrixTheory. We compute the weak localization corrections to the mixed cumulants ofthe conductance and shot noise for beta=1,4, thus proving a number ofconjectures of Khoruzhenko et al. (Phys. Rev. B, Vol. 80 (2009), 125301). Wederive differential equations that characterize the cumulant generatingfunctions for all beta=1,2,4. Furthermore, we show that the cumulant generatingfunction of the Wigner delay time can be expressed in terms of the Painleve'III' transcendant. This allows us to study properties of the cumulants of theWigner delay time in the asymptotic limit n -> infinity. Finally, for all thesymmetry classes and for any number of open channels, we derive a set ofrecurrence relations that are very efficient for computing cumulants at allorders.

Tau-Function Theory of Quantum Chaotic Transport with beta=1,2,4