# SUBADDITIVE COCYCLES AND HOROFUNCTIONS

@article{Gouzel2019SUBADDITIVECA, title={SUBADDITIVE COCYCLES AND HOROFUNCTIONS}, author={S{\'e}bastien Gou{\"e}zel}, journal={Proceedings of the International Congress of Mathematicians (ICM 2018)}, year={2019} }

Subadditive cocycles are the random version of subadditive sequences. They play an important role in probability and ergodic theory, notably through Kingman’s theorem ensuring their almost sure convergence. We discuss a variation around Kingman’s theorem, showing that a subadditive cocycle is in fact almost additive at many times. This result is motivated by the study of the iterates of deterministic or random semicontractions on metric spaces, and implies the almost sure existence of a…

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