PreprintCharacteristic polynomial patterns in difference sets of matricesM. Bjorklund, A. FishAbstractWe show that for every subset \(E\) of positive density in the set of integer squarematrices with zero traces, there exists an integer \(k\geqslant 1\) such that the set of characteristic polynomials of matrices in \(EE\) contains the set of all characteristic polynomials of integer matrices with zero traces and entries divisible by \(k\). Our theorem is derived from results by BenoistQuint on measure rigidity for actions on homogeneous spaces. Keywords: Ergodic Ramsey Theory, Measure rigidity.AMS Subject Classification: Primary: 37A45; Secondary: 11P99, 11C99.
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