395 citations · 2.7k across the 108 of their papers we have counts for
13 papers · 1 filter
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…
Simply Exponential Approximation of the Permanent of Positive Semidefinite Matrices
Nima Anari, Leonid Gurvits, Shayan Oveis Gharan +1
We design a deterministic polynomial time approximation algorithm for the permanent of positive semidefinite matrices where . We write a natural convex…
Bounds on the permanent and some applications
Leonid Gurvits, Alex Samorodnitsky
We give new lower and upper bounds on the permanent of a doubly stochastic matrix. Combined with previous work, this improves on the deterministic approximation factor for the perm…
Unleashing the power of Schrijver's permanental inequality with the help of the Bethe Approximation
Leonid Gurvits
Let be doubly-stochastic matrix. Alexander Schrijver proved in 1998 the following remarkable inequality per(\widetilde{A}) \geq \prod_{1 \leq i,j \leq n} (…
On multivariate Newton-like inequalities
Leonid Gurvits
We study multivariate entire functions and polynomials with non-negative coefficients. A class of {\bf Strongly Log-Concave} entire functions, generalizing {\it Minkowski} volume p…
A short, based on the mixed volume, proof of Liggett's theorem on the convolution of ultra-logconcave sequences
Leonid Gurvits
R. Pemantle conjectured, and T.M. Liggett proved in 1997, that the convolution of two ultra-logconcave is ultra-logconcave. Liggett's proof is elementary but long. We present here…