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Mathematical Research Letters
Volume 26 (2019)
Number 2
Lyapunov exponents of the Brownian motion on a Kähler manifold
Pages: 501 – 536
DOI: https://dx.doi.org/10.4310/MRL.2019.v26.n2.a6
Authors
Abstract
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 $\mathbb{P}(E)$. 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.
Received 18 January 2018
Accepted 1 May 2018
Published 12 August 2019