This is an announcement for the paper "Ramanujan graphs and the solution of the Kadison-Singer problem" by Adam W. Marcus, Daniel A. Spielman, and Nikhil Srivastava,.
Abstract: We survey the techniques used in our recent resolution of the Kadison-Singer problem and proof of existence of Ramanujan Graphs of every degree: mixed characteristic polynomials and the method of interlacing families of polynomials. To demonstrate the method of interlacing families of polynomials, we give a simple proof of Bourgain and Tzafriri's restricted invertibility principle in the isotropic case.
Archive classification: math.SP math.CO math.OA
Mathematics Subject Classification: 05C50, 46L05, 26C10
Remarks: A version of this paper will appear in the proceedings of the 2014
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1408.4421
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