Lyapunov exponents of the Brownian motion on a Kähler manifold

Daniel, Jeremy; Deroin, Bertrand

doi:10.4310/MRL.2019.v26.n2.a6

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Lyapunov exponents of the Brownian motion on a Kähler manifold

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Daniel, Jeremy
Max Planck Institute for Mathematics, Max Planck Society;

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http://dx.doi.org/10.4310/MRL.2019.v26.n2.a6
(Publisher version)

https://doi.org/10.48550/arXiv.1702.02551
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Citation

Daniel, J., & Deroin, B. (2019). Lyapunov exponents of the Brownian motion on a Kähler manifold. Mathematical Research Letters, 26(2), 501-536. doi:10.4310/MRL.2019.v26.n2.a6.

Cite as: https://hdl.handle.net/21.11116/0000-0004-C5EB-5

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 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.