On Determinants of Constrained Random Fourier Minors
نویسندگان
چکیده
ABSTRACT. For parameters n, l and r, we consider the problem of maximizing the determinant of an l × l Vandermonde matrix V, with nodes selected from the set Ωn of nth roots of unity, but avoiding a forbidden subset R of size r. An asymptotically tight lower bound is given for the expected value of ln |detV | in case the nodes are selected uniformly at random from Ωn/R. We apply our result to give a discrete uncertainty relation for so-called ǫ, l-index-limited vectors.
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