Mixed determinants and the Kadison–Singer problem

@article{Ravichandran2016MixedDA,
  title={Mixed determinants and the Kadison–Singer problem},
  author={M. Ravichandran and J. Leake},
  journal={Mathematische Annalen},
  year={2016},
  volume={377},
  pages={511-541}
}
  • M. Ravichandran, J. Leake
  • Published 2016
  • Mathematics
  • Mathematische Annalen
  • We adapt the arguments of Marcus, Spielman and Srivastava in their proof of the Kadison–Singer problem to prove improved paving estimates. Working with Anderson’s paving formulation of Kadison–Singer instead of Weaver’s vector balancing version, we show that the machinery of interlacing polynomials due to Marcus, Spielman and Srivastava works in this setting as well. The relevant expected characteristic polynomials turn out to be related to the so called “mixed determinants” that have been… CONTINUE READING
    Asymptotically Optimal Multi-Paving
    • 2
    • PDF
    The Kadison-Singer Problem
    • 4
    • PDF
    An analytical Lieb-Sokal lemma
    X-Ramanujan Graphs
    • 2
    • PDF

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 30 REFERENCES
    Hyperbolic polynomials and the Marcus-Spielman-Srivastava theorem
    • 10
    • PDF
    Solutions to two problems on permanents
    • 9
    • PDF
    Linear matrix inequality representation of sets
    • 285
    • PDF
    Negative dependence and the geometry of polynomials
    • 177
    • PDF
    The Complexity of the Fermionant and Immanants of Constant Width [Note]
    • 13
    • PDF