On Cocycles over Ergodic Transformations and Barycenters

Key Points

• The research aims to classify linear cocycles using barycenters of measures on boundaries of symmetric spaces.
• Application of barycenters of measures
• Analysis of linear cocycles over ergodic transformations
• Consideration of semisimple Lie groups of rank 1
• Examination of recurrence of stationary random walks
• Establishment of a framework for classifying linear cocycles
• Connections identified between barycenters and ergodic transformations
• Insights into the recurrence of random walks on specific Lie groups