2014/08/19 by Marcus, Adam W., Spielman, Daniel A., Srivastava, Nikhil
#05C50 #26C10 #46L05 #Combinatorics (math.CO) #FOS: Mathematics #Operator Algebras (math.OA) #Spectral Theory (math.SP)
paper · doi:10.48550/arxiv.1408.4421
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.