Improved spectral gap bounds on positively curved manifolds

Laurent Veysseire (1)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

A coupling method and an analytic one allow us to prove new lower bounds for the spectral gap of reversible diffusions on compact manifolds. Those bounds are based on the a notion of curvature of the diffusion, like the coarse Ricci curvature or the Bakry--Emery curvature-dimension inequalities. We show that when this curvature is nonnegative, its harmonic mean is a lower bound for the spectral gap.

Domaines: Probabilités [math.PR]; Géométrie différentielle [math.DG]

Laurent Veysseire. Improved spectral gap bounds on positively curved manifolds. 2011. ⟨hal-00596725⟩