Ramanujan Graphs and the Solution of the Kadison-Singer Problem

Adam W. Marcus; Daniel A. Spielman; Nikhil Srivastava

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arXiv · 1408.4421

Ramanujan Graphs and the Solution of the Kadison-Singer Problem

Adam W. Marcus·Daniel A. Spielman·Nikhil Srivastava

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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.

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Adam W. Marcus, Daniel A. Spielman, Nikhil Srivastava. 2014-08-19. Ramanujan Graphs and the Solution of the Kadison-Singer Problem. https://arxiv.org/abs/1408.4421

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