Random concave functions

Spaces of convex and concave functions appear naturally in theory applications. For example, regression log-concave density estimation are important topics nonparametric statistics. In stochastic portfolio theory, on the unit simplex measure concentration capital, their gradient maps define novel investment strategies. The may also be regarded as optimal transport simplex. this paper we construct study probability measures supported spaces functions. These serve prior distributions Bayesian statistics Cover’s universal portfolio, induce distribution-valued random variables via transport. constructed by taking a suitably scaled (mollified, or soft) minimum hyperplanes. Depending regime parameters, show that number hyperplanes tends to infinity there several possible limiting behaviors. particular, is transition from deterministic almost sure limit nontrivial distribution can characterized using duality Poisson point processes.