6 papers · 1 filter
An Explicit Family of Log-Concave Counterexamples to the Gaussian Completely Monotone Conjecture
Jiayang Zou, Luyao Fan, Jiayang Gao +1
We construct smooth, strictly log-concave counterexamples to the Gaussian completely monotone conjecture in every dimension. In one dimension, they form an explicit family wh…
A Hexagonal Counterexample to Log-Convexity of Fisher Information Along the Heat Flow
Jiayang Zou, Luyao Fan, Jiayang Gao +1
We construct a smooth, strictly positive, Gaussian-decaying density on for which Fisher information along the heat flow is not log-convex. This disproves the Cheng--…
Rate-distortion Theory with Lower Semi-continuous Distortion on Noncompact Alphabets
Jiayang Zou, Luyao Fan, Jiayang Gao +1
In this paper, we study rate-distortion theory for general sources with an emphasis on the existence of optimal reconstruction distributions on noncompact alphabets. Classical atta…
A Revisit to Rate-distortion Theory via Optimal Weak Transport
Jiayang Zou, Luyao Fan, Jiayang Gao +1
This paper revisits the rate-distortion theory from the perspective of optimal weak transport, as recently introduced by Gozlan et al. While the conditions for optimality and the e…
Convexity of Mutual Information along the Fokker-Planck Flow
Jiayang Zou, Luyao Fan, Jiayang Gao +1
We study the convexity of mutual information as a function of time along the Fokker-Planck flow. The results are generalizations of that along heat flow and Ornstein-Ulenbeck flow,…
Differential Properties of Information in Jump-diffusion Channels
Luyao Fan, Jiayang Zou, Jiayang Gao +1
We propose a channel modeling using jump-diffusion processes, and study the differential properties of entropy and mutual information. By utilizing the Kramers-Moyal and Kolmogorov…