Hyperbolicity and stable polynomials in combinatorics and probability

By Robin Pemantle. 2012

63 citations recorded by the source corpus.

These lectures survey the theory of hyperbolic and stable polynomials, from their origins in the theory of linear PDE’s to their present uses in combinatorics and probability theory.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/03c512cbf7ad528a7cc344b2b812a3bc1897ec87

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

1. Adam W. Marcus
2. Daniel A. Spielman
3. Nikhil Srivastava
4. David P. Woodruff
5. Roman Vershynin
6. Einar Steingrímsson

In Geometry and Topology

1. Adam W. Marcus
2. Nikhil Srivastava
3. Daniel A. Spielman
4. David P. Woodruff
5. Roman Vershynin
6. Jalaj Upadhyay

In Mathematical Physics

1. Adam W. Marcus
2. Daniel A. Spielman
3. Nikhil Srivastava

Citations in the corpus

• Interlacing families II: Mixed characteristic polynomials and the Kadison{Singer problem (2013, background): “There are many operations that are known to preserve real stability and real-rootedness of polynomials (see [39], [16], [18], [19], [44, 48]).”
• Interlacing Families I: Bipartite Ramanujan Graphs of All Degrees (2013, background): “We have shown that for certain special polynomial-valued random variables P : Ω → R [ x ], there must be an ω with λ max ( P ( ω )) ≤ λ max ( E [ P ]).”