Here's a link to the referenced paper where Marcus, Spielman, and Srivastava present their proof: "Interlacing Families II: Mixed Characteristic Polynomials an

Here's a link to the referenced paper where Marcus, Spielman, and Srivastava present their proof: "Interlacing Families II: Mixed Characteristic Polynomials and the Kadison-Singer Problem" http://arxiv.org/pdf/1306.3969v4.pdf http://arxiv.org/pdf/1306.3969v4.pdf