7 papers
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 vect…
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…
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 be…
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…
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…