Interlacing families II: Mixed characteristic polynomials and the Kadison{Singer problem

By Adam W. Marcus, Daniel A. Spielman, Nikhil Srivastava. 2013

545 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/4ef20b61b0eb49d2dabaefa2f27756ddaa1e8fd1

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In Algebra and Number Theory

In Computational Theory and Mathematics

In Electrical and Electronic Engineering

Citations in the corpus

Iterative actions of normal operators (2016, methodology): “1 was conjectured by Feichtinger and is equivalent to the Kadison-Singer theorem [8, 7] which was proved recently in [30].”
On spectral Cantor-Moran measures and a variant of Bourgain's sum of sine problem (2019, methodology): “A way to construct a frame triple tower is to use the Kadison-Singer theorem [35] (see also [15] for some recent advance).”
Unimodality, log-concavity, real-rootedness and beyond (2015, methodology): “lem in combinatorics is Gurvits proof of a vast generalization of the Van der Waerden conjecture, [54]. A recent application is the spectacular solution to the Kadison{Singer problem by Marcus et al. [67]. See the surveys [76,104] for further applications of stable polynomials. The notion of HPP and”
Polynomial convolutions and (nite) free probability (2021, methodology): “The purpose of this paper was to draw the connection between the recent work of the author with Daniel Spielman and Nikhil Srivastava [17, 18, 19, 20, 21] with free probability and more traditional random matrix theory.”
Structured Random Matrices (2016, unknown): “oes not provide any useful tool in random matrix theory. Nonetheless, a determinisitic version of this idea plays the crucial role in the recent breakthroughresolution of the KadisonSinger conjecture [15], so that it is conceivable that such an approach could prove to be fruitful in problems of rand”
Interlacing Families I: Bipartite Ramanujan Graphs of All Degrees (2013, methodology): “This is the same (up to normalization) as the Stieltjes transform and the “barrier function” of [2], [11], [12].”
Frame properties of systems arising via iterated actions of operators (2019, methodology): “Technically our main tool is the Feichtinger Conjecture, which has been confirmed in [18] and therefore now is a theorem.”
Operator Representations of Frames: Boundedness, Duality, and Stability (2017, methodology): “The proof uses the Feichtinger theorem (which was a conjecture for several years and finally got confirmed in [15]).”