6 papers
Two-Parameter Rényi Information Quantities with Applications to Privacy Amplification and Soft Covering
Shi-Bing Li, Ke Li, Lei Yu
There are no universally accepted definitions of Rényi conditional entropy and Rényi mutual information, although motivated by different applications, several definitions have been…
Large Deviations Principle for Isoperimetry and Its Equivalence to Nonlinear Log-Sobolev Inequalities
Lei Yu
The isoperimetric problem is a classic topic in geometric measure theory, yet critical questions regarding the characterization of optimal solutions -- even asymptotically optimal…
On Average Distance, Level-1 Fourier Weight, and Chang's Lemma
Lei Yu
In this paper, we improve the well-known level-1 weight bound, also known as Chang's lemma, by using an induction method. Our bounds are close to optimal no matter when the set is…
Regularity of solutions to time-harmonic Maxwell's system with Hölder and various lower than Hölder continuous coefficients
Lei Yu, Basang Tsering-xiao
The purpose of this paper is to establish a complete Schauder theory for the second-order linear elliptic equation and the time-harmonic Maxwell's system. We prove global Hölder re…
Local Optimality of Dictator Functions with Applications to Courtade--Kumar and Li--Médard Conjectures
Lei Yu
Given a convex function , the -stability of a Boolean function is defined as , where is a random vector u…
Large Deviation Analysis for the Reverse Shannon Theorem
Shi-Bing Li, Ke Li, Lei Yu
Channel simulation is to simulate a noisy channel using noiseless channels with unlimited shared randomness. This can be interpreted as the reverse problem to Shannon's noisy codin…