Propagation of weak log-concavity along generalised heat flows via Hamilton-Jacobi equations

Vortrag von Dr. Giovanni Conforti

Datum: 20.05.26  Zeit: 17.15 - 18.45  Raum: Y27H12

A classical consequence of the Prékopa–Leindler inequality is that log-concavity is preserved along the heat flow. Beyond the classical heat semigroup, however, this phenomenon typically breaks down. 

In this talk, I will introduce a weaker notion of log-concavity that remains stable under generalized heat semigroups. I will show how this framework yields new log-semiconcavity estimates for ground states of Schrödinger operators with non-convex potentials, as well as propagation results for functional inequalities along generalized heat flows.I will also discuss how these weak log-concavity properties behave under conditioning and marginalization, extending classical ideas of Brascamp and Lieb beyond the log-concave setting. 

The main ingredient is a stochastic control perspective on quadratic Hamilton–Jacobi–Bellman equations, combined with a second-order analysis of reflection couplings along HJB characteristics.