5 citations · 22 across the 12 of their papers we have counts for
7 papers · 1 filter
Lorentzian polynomials on cones
Petter Brändén, Jonathan Leake
Inspired by the theory of hyperbolic polynomials and Hodge theory, we develop the theory of Lorentzian polynomials on cones. This notion captures the Hodge-Riemann relations of deg…
Lorentzian polynomials on cones and the Heron-Rota-Welsh conjecture
Petter Brändén, Jonathan Leake
We give a short proof of the log-concavity of the coefficients of the reduced characteristic polynomial of a matroid. The proof uses an extension of the theory of Lorentzian polyno…
Lower bounds for contingency tables via Lorentzian polynomials
Petter Brändén, Jonathan Leake, Igor Pak
We present a new lower bound on the number of contingency tables, improving upon and extending previous lower bounds by Barvinok and Gurvits. As an application, we obtain new lower…
Capacity Lower Bounds via Productization
Leonid Gurvits, Jonathan Leake
We give a sharp lower bound on the capacity of a real stable polynomial, depending only on the value of its gradient at . This result implies a sharp improvement to a simila…
On the Further Structure of the Finite Free Convolutions
Jonathan Leake, Nick Ryder
Since the celebrated resolution of Kadison-Singer (via the Paving Conjecture) by Marcus, Spielman, and Srivastava, much study has been devoted to further understanding and generali…
Counting Matchings via Capacity Preserving Operators
Leonid Gurvits, Jonathan Leake
The notion of the capacity of a polynomial was introduced by Gurvits around 2005, originally to give drastically simplified proofs of the Van der Waerden lower bound for permanents…