The theory of Group Representations is often useful when studying expected characteristic polynomials. For example, it can be used to solve the following question: if one takes a 0-1 matrix and blows it up so that every 0 entry becomes a dxd zero block, and every 1 entry becomes a dxd random permutation matrix, what is the expected characteristic polynomial? I plan to describe some of these applications of group representations, and also to present some relevant open problems.
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