Brownian Motion on the Unitary Quantum Group: Construction and Cutoff

1. Characterize the singular part of the limit distribution in the loss-of-absolute-continuity regime (c < 0) for Brownian motion on U_N^+ 
2. Applicability of Biane’s recovery method in the non-atomic singular case for U_N^+ 
3. Conjecture on singular support and L^1-convergence of the absolutely continuous part for c < 0 

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