11 papers
An explicit dimension-free isoperimetric plateau in the cube
Lei Yu
We prove that, in every dimension, the relative Euclidean isoperimetric profile of the unit cube equals one whenever the prescribed volume differs from one half by at most $6.25\ti…
Sharp Small-Volume Isoperimetry from Log-Sobolev Inequalities
Lei Yu
Let be the asymptotic isoperimetric profile for product of a weighted Riemannian manifold satisfying $\mathrm{CD}(0,\i…
A Sharp Small-Coefficient Variant of Khintchine's Inequality and the Sharp Theorem
Lei Yu
We prove a refined quadratic normal approximation for the first absolute moment of normalized weighted Rademacher sums with bounded maximal coefficients. For any weight vector $w\i…
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…
Functional inequalities and random walks on increasing subsets of the hypercube
Fan Chang, Guowei Sun, Lei Yu
Motivated by random walks on subsets of the hypercube, we prove two discrete functional inequalities on the hypercube by the technique of induction-by-restrictions. First, we give…
On Average Distance, Level-1 Fourier Weight, and Chang's Lemma
Lei Yu
We study the maximum level- Fourier weight of Boolean functions, which is equivalent to the minimum average-distance problem on the hypercube. We first determine the dimension-f…
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…
Rényi Common Information for Doubly Symmetric Binary Sources
Lei Yu
In this note, we provide analytic expressions for the Rényi common information of orders in for the doubly symmetric binary source (DSBS). Until now, analytic expressi…