Limiting spectral distribution of the product of truncated Haar unitary matrices
Random Matrices: Theory and Application
Let An(i), 1 ≤ i ≤ k, be k probabilistically independent matrices of order ni × ni+1 (with n1 = nk+1) which are the left-uppermost blocks of n × n Haar unitary matrices. Suppose that n ni → αi as n →∞, with 1 < αi < ∞. Using free probability and Brown measure techniques, we find the limiting spectral distribution of An(1)⋯A n(k).
Adhikari, Kartick and Bose, Arup, "Limiting spectral distribution of the product of truncated Haar unitary matrices" (2020). Journal Articles. 342.