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From one perspective, free probability is the study of how the eigenvalues of large random matrices interact under the basic matrix operations. The free probability operations of free additive ...

Any unitary matrix $U$ can be diagonalized by another unitary matrix $V$, $$U=VDV^\dagger,$$ where $D={\rm diag}(z_1,z_2,...,z_N)$ is diagonal. If $U$ is taken at random uniformly with respect to Haar ...

Given that one can sample unitaries from the Haar measure over $U(n)$ (as in F. Mezzadri, Notices of the AMS 54 (2007), 592-604), how can one sample from the uniform distribution over the following ...

An answer to another question derived a formula for the volume of a delta-ball in $O(n)$. I am wondering if there is a (constructive) way to draw samples uniformly at random from such a region. For ...