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Everything the deals with properties and definitions of Haar measure, as well as related fields when the question relies heavily on the notion of haar measure - group harmonic analysis, group ergodic theory etc.

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Biased ensemble in the unitary group

I am interested in studying the ensemble of unitary random matrices in $U(L)$ made as follows $$ \mu(U)=\frac{1}{\mathcal{Z}[\omega]}\mu_{\rm Haar}(U) e^{-\sum_{k=1}^L \sum_{l=1}^N \omega_k |U_{kl}|^2 …