Combinatorics of Truncated Random Unitary Matrices


We investigate the combinatorics of truncated Haar-distributed random unitary matrices. Specifically, if U is a random matrix from the unitary group U(d), let Uk denote its k × k upper left corner, where 1 ≤ k ≤ d. We give an explicit combinatorial formula for the moments ∫ U(d) |Tr(Uk)|dU in terms of pairs of Standard Young Tableaux on shapes that are not neccessarily the same. This formula can be restated as counting configurations of non-intersecting walkers on the integer lattice. Our main tool is the ColourFlavour transformation of Lattice Gauge Theory.

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@inproceedings{Novak2008CombinatoricsOT, title={Combinatorics of Truncated Random Unitary Matrices}, author={Jonathan Novak}, year={2008} }