5 citations · 22 across the 12 of their papers we have counts for
15 papers
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…
Deterministic Approximation Algorithms for Volumes of Spectrahedra
Mahmut Levent Doğan, Jonathan Leake, Mohan Ravichandran
We give a method for computing asymptotic formulas and approximations for the volumes of spectrahedra, based on the maximum-entropy principle from statistical physics. The method g…
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…
Optimization and Sampling Under Continuous Symmetry: Examples and Lie Theory
Jonathan Leake, Nisheeth K. Vishnoi
In the last few years, the notion of symmetry has provided a powerful and essential lens to view several optimization or sampling problems that arise in areas such as theoretical c…
On the Computability of Continuous Maximum Entropy Distributions: Adjoint Orbits of Lie Groups
Jonathan Leake, Nisheeth K. Vishnoi
Given a point in the convex hull of a given adjoint orbit of a compact Lie group , we give a polynomial time algorithm to compute the probability density su…
Sampling Matrices from Harish-Chandra-Itzykson-Zuber Densities with Applications to Quantum Inference and Differential Privacy
Jonathan Leake, Colin S. McSwiggen, Nisheeth K. Vishnoi
Given two Hermitian matrices and , the Harish-Chandra-Itzykson-Zuber (HCIZ) distribution on the unitary group is , whe…