Lyapunov exponents of the Brownian motion on a Kähler manifold

Jeremy Daniel (1) , Bertrand Deroin (2)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 AGM - UMR 8088 - Analyse, Géométrie et Modélisation

If E is a flat bundle of rank r over a Kähler manifold X, we define the Lyapunov spectrum of E: a set of r numbers controlling the growth of flat sections of E, along Brownian trajectories. We show how to compute these numbers, by using harmonic measures on the foliated space P(E). Then, in the case where X is compact, we prove a general inequality relating the Lyapunov exponents and the degrees of holomorphic subbundles of E and we discuss the equality case.

Domaines: Mathématiques [math]

Jeremy Daniel, Bertrand Deroin. Lyapunov exponents of the Brownian motion on a Kähler manifold. Mathematical Research Letters, 2019. ⟨hal-03060434⟩