Highly Influential

3 Excerpts

- Published 2008

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.

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