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We develop bounds for the second largest eigenvalue and spectral gap
of a reversible Markov chain. The bounds depend on geometric quantities
such as the maximum degree, diameter and covering numbe...
Tight Oracle Bounds for Low-rank Matrix Recovery from a Minimal Number of Random Measurements
Matrix completion The Dantzig selector oracle inequalities norm of random matrices convex optimization and semidefinite programming
2015/6/17
This paper presents several novel theoretical results regarding the recovery of a low-rank matrix from just a few measurements consisting of linear combinations of the matrix entries. We show that pro...
Bounds on volume growth of geodesic balls under Ricci flow
geodesic balls under Ricci flow Differential Geometry Analysis of PDEs
2011/9/16
Abstract: We prove a so called $\kappa$ non-inflating property for Ricci flow, which provides an upper bound for volume ratio of geodesic balls over Euclidean ones, under an upper bound for scalar cur...
Abstract: In 2008, Bukh, Matousek, and Nivasch conjectured that for every n-point set S in R^d and every k, 0 <= k <= d-1, there exists a k-flat f in R^d (a "centerflat") that lies at "depth" (k+1) n ...
Existence and a priori bounds for electrostatic Klein-Gordon-Maxwell systems in fully inhomogeneous spaces
Existence electrostatic Klein-Gordon-Maxwell systems fully inhomogeneous spaces
2011/2/22
We prove existence and uniform bounds for electrostatic Klein-Gordon-Maxwell systems in the inhomogeneous context of a compact Riemannian manifold when the mass potential, balanced by the phase, is sm...
Lower and upper bounds for nef cones
nef cones
2010/11/26
The nef cone of a projective variety Y is an important and often elusive invariant. In this paper we construct two polyhedral lower bounds and one polyhedral upper bound for the nef cone of Y using an...
New Bounds for The Identric Mean of Two Arguments
Arithmetic mean Geometric mean Identric mean
2010/1/22
Given two positive real numbers and , let , , and denote their arithmetic mean, geometric mean, and identric mean, respectively. Also, let for . In this note we prove that for all positive real...