Work

Stationary probability measures on projective spaces 2: The critical case

Year: 2025

Type: article

Abstract: In a previous article, given a finite-dimensional real vector space V and a probability measure μ on PGL(V) with finite first moment, we gave a description of all μ-stationary probability measures on the projective space P(V) in the noncritical (or Lyapunov dominated) case. In the current article, we complete the analysis by providing a full description of the more subtle critical case. Our results demonstrate an algebraic rigidity in this situation. Combining our results with those of Furstenberg and Kifer, Guivarch and Raugi, and Benoist and Quint, we deduce a classification of all stationary probability measures on the projective space for independent and identically distributed random matrix products with finite first moment without any algebraic assumption.

Source: Duke Mathematical Journal

DOI: 10.1215/00127094-2024-0056

Authors: Richard Aoun, Cagri Sert

Institutions: Laboratoire d’Analyse et de Mathématiques Appliquées, Université Gustave Eiffel, University of Warwick

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung

Award: Fractals, counting and approximation