4 papers · 1 filter
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…