DIFFUSION BY OPTIMAL TRANSPORT IN HEISENBERG GROUPS

Nicolas Juillet (1, 2)

1 IF - Institut Fourier
2 Institut für angewandte Mathematik

We prove that the hypoelliptic diffusion of the Heisenberg group Hn describes, in the space of probability measures over Hn a gradient flow of the Boltzmann entropy Ent_\infty in the sense of optimal transport. We prove that conversely any gradient flow of Ent_\infty that satisfy a further derivability assumption satisfy the hypoelliptic heat equation.

Mots clés: espace de Wasserstein; diffusion hypoelliptique; groupe de Heisenberg

Domaines: Probabilités [math.PR]; Géométrie métrique [math.MG]

Nicolas Juillet. DIFFUSION BY OPTIMAL TRANSPORT IN HEISENBERG GROUPS. 2009. ⟨hal-00372216v1⟩