@article{Gouzel2019SUBADDITIVECA,
author={S{\'e}bastien Gou{\"e}zel},
journal={Proceedings of the International Congress of Mathematicians (ICM 2018)},
year={2019}
}
• S. Gouëzel
• Published 1 May 2019
• Mathematics
• Proceedings of the International Congress of Mathematicians (ICM 2018)
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…
6 Citations

## Figures from this paper

Hahn-Banach for metric functionals and horofunctions
• A. Karlsson
• Mathematics
Journal of Functional Analysis
• 2021
Wolff–Denjoy theorems in geodesic spaces
• Mathematics
Bulletin of the London Mathematical Society
• 2021
We show a Wolff–Denjoy type theorem in complete geodesic spaces in the spirit of Beardon's framework that unifies several results in this area. In particular, it applies to strictly convex bounded
Comments on the cosmic convergence of nonexpansive maps
• Materials Science
Journal of fixed point theory and Its applications
• 2021
Using metric functionals, a connection to the invariant subspace problem is made and a new result for nonexpansive maps of documentclass[12pt]{minimal] is proved.
Characterizing the metric compactification of $$L_{p}$$ spaces by random measures
<jats:p>We present a complete characterization of the metric compactification of <jats:inline-formula><jats:alternatives><jats:tex-math>$$L_{p}$$</jats:tex-math><mml:math
Modelling High-Level Mathematical Reasoning in Mechanised Declarative Proofs
• Computer Science
ArXiv
• 2020
A non-synthetic dataset is built from the largest repository of mechanised proofs and a task on causal reasoning, where a model is required to fill in a missing intermediate proposition given a causal context, and a hierarchical transformer model is proposed that outperforms the transformer baseline.
The metric compactification of $L_{p}$ represented by random measures
We present a complete characterization of the metric compactification of $L_{p}$ for all $1 \leq p < \infty$. Each element of the metric compactification of $L_{p}$ is represented by a random measure

## References

SHOWING 1-10 OF 17 REFERENCES
• Mathematics
Journal of the European Mathematical Society
• 2020
A result for subadditive ergodic cocycles is proved that provides more delicate information than Kingman's subadditive ergodic theorem. As an application we deduce a multiplicative ergodic theorem
A Multiplicative Ergodic Theorem and Nonpositively Curved Spaces
• Mathematics
• 1999
Abstract:We study integrable cocycles u(n,x) over an ergodic measure preserving transformation that take values in a semigroup of nonexpanding maps of a nonpositively curved space Y, e.g. a
Non-expanding maps and Busemann functions
• A. Karlsson
• Mathematics
Ergodic Theory and Dynamical Systems
• 2001
We give stronger versions and alternative simple proofs of some results of Beardon, [Be1] and [Be2]. These results concern contractions of locally compact metric spaces and generalize the theorems of
What is ergodic theory
Ergodic theory involves the study of transformations on measure spaces. Interchanging the words “measurable function” and “probability density function” translates many results from real analysis to
Asymptotic behavior of nonexpansive mappings in normed linear spaces
• Mathematics
• 1981
LetT be a nonexpansive mapping on a normed linear spaceX. We show that there exists a linear functional.f, ‖f‖=1, such that, for allx∈X, limn→xf(Tnx/n)=limn→x‖Tnx/n‖=α, where α≡infy∈c‖Ty-y‖. This
Metric Spaces Of Non Positive Curvature
The metric spaces of non positive curvature is universally compatible with any devices to read and is available in the digital library an online access to it is set as public so you can download it instantly.