6 papers
Unique Minimizers for Permanents, Mixed Discriminants, and Log-concave Polynomials
Leonid Gurvits, Jonathan Leake
The permanent and mixed discriminant of positive matrices are classic problems for which we do not expect an efficient algorithm for exact computation. Thus much work has been done…
Trickle-down Theorems via C-Lorentzian Polynomials II: Pairwise Spectral Influence and Improved Dobrushin's Condition
Jonathan Leake, Shayan Oveis Gharan
Let be a probability distribution on a multi-state spin system on a set of sites; equivalently, a -partite simplicial complex with distribution on maximal faces. For…
Optimal Trickle-Down Theorems for Path Complexes via C-Lorentzian Polynomials with Applications to Sampling and Log-Concave Sequences
Jonathan Leake, Kasper Lindberg, Shayan Oveis Gharan
Let be a -partite -dimensional simplicial complex with parts and let be a distribution on the facets of . Informally, we say is a path comp…
Inequalities characterizing distinguished unipotent orbits
Alexander Bertoloni Meli, Teruhisa Koshikawa, Jonathan Leake
In this paper we prove a new characterization of the distinguished unipotent orbits of a connected reductive group over an algebraically closed field of characteristic 0. For class…
Compatibility of Real-Rooted Polynomials with Mixed Signs
Jonathan Leake, Nick Ryder
We characterize compatible families of real-rooted polynomials, allowing both positive and negative leading coefficients. Our characterization naturally generalizes the same-sign c…
From Trees to Polynomials and Back Again: New Capacity Bounds with Applications to TSP
Leonid Gurvits, Nathan Klein, Jonathan Leake
We give simply exponential lower bounds on the probabilities of a given strongly Rayleigh distribution, depending only on its expectation. This resolves a weak version of a problem…