On Cocycles over Ergodic Transformations and Barycenters

The barycenters of measures on boundaries of symmetric spaces are applied for classification of linear cocycles over ergodic transformations. We also consider the case of semisimple Lie groups of rank $1$ and recurrence of stationary random walks on them.

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Publication Details

Journal
Theory of Probability and Its Applications
Published
2026-02-01
DOI
https://doi.org/10.1137/s0040585x97t99263x
Primary Topic
advanced mathematical theories
Type
article
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article

On Cocycles over Ergodic Transformations and Barycenters

M. E. Lipatov
Theory of Probability and Its Applications
advanced mathematical theories
article

On Cocycles over Ergodic Transformations and Barycenters

M. E. Lipatov
article en

Abstract

The barycenters of measures on boundaries of symmetric spaces are applied for classification of linear cocycles over ergodic transformations. We also consider the case of semisimple Lie groups of rank $1$ and recurrence of stationary random walks on them.

Theory of Probability and Its ApplicationsVol. 70(4)
Openalex Percentile: Top 45%
advanced mathematical theories
DOISourceOpenAlex
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On Cocycles over Ergodic Transformations and Barycenters — M. E. Lipatov · Theory of Probability and Its Applications (2026) | TGRS Research Map | TGRS