Convexity of mutual information along the Ornstein-Uhlenbeck flow
Convexity of mutual information along the Ornstein-Uhlenbeck flow
We study the convexity of mutual information as a function of time along the flow of the Ornstein-Uhlenbeck process. We prove that if the initial distribution is strongly log-concave, then mutual information is eventually convex, i.e., convex for all large time. In particular, if the initial distribution is sufficiently strongly …