Ramanujan Graphs and the Solution of the Kadison–Singer Problem
نویسندگان
چکیده
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. Mathematics Subject Classification (2010). Primary, 05C50, 46L05; Secondary, 26C10.
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