Time delay statistics for finite number of channels in all symmetry classes

Within a random matrix theory approach, we obtain spectral statistics of the Wigner time delay matrix $Q$, for arbitrary channels number $M$ and for all symmetry classes, in fact for general Dyson parameter $β$. We also put forth two conjectures: one is related to the large-$M$ expansion of joint cumulants of traces of powers of $Q$, which generalizes and implies a previous conjecture of Cunden, Mezzadri, Vivo and Simm; the other concerns the tail of the distribution of traces of powers of $Q$.

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