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Random Unitary Matrices with Structure
Prof. Brendan Farrell(California Institute of Technology, USA)
2018-01-01 12:13  华东师范大学

Matrices with uniform distribution on the set of unitary matrices are the cannonical type of matrix to work with in many settings. For example, selecting a random subset of the columns of such a matrix gives a uniform distribution on subspaces of a certain dimension. Yet, there are distributions on the set of unitary matrices that allow for more structure and less randomness while still retaining important properties of uniformly distributed random unitary matrices. We present recent results for unitary matrices constructed using a Hadamard matrix and a signed permutation matrix or Kronecker products of a uniformly distributed unitary matrix. The structured approach also very naturally leads to formulations of discrete uncertainty principles. This is joint work with G. Anderson and R.R. Nadakuditi.