Random 2D linear cocycles II: statistical properties
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866908593131880448 |
|---|---|
| author | Duarte, Pedro Durães, Marcelo Graxinha, Tomé Klein, Silvius |
| author_facet | Duarte, Pedro Durães, Marcelo Graxinha, Tomé Klein, Silvius |
| contents | Consider the space of two dimensional random linear cocycles over a shift in finitely many symbols, with at least one singular and one invertible matrix. We provide an explicit formula for the unique stationary measure associated to such cocycles and establish a Furstenberg-type formula characterizing the Lyapunov exponent. Using the spectral properties of the corresponding Markov operator and a parameter elimination argument, we prove that Lebesgue almost every cocycle in this space satisfies large deviations estimates and a central limit theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_00146 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Random 2D linear cocycles II: statistical properties Duarte, Pedro Durães, Marcelo Graxinha, Tomé Klein, Silvius Dynamical Systems Mathematical Physics 37A30 Consider the space of two dimensional random linear cocycles over a shift in finitely many symbols, with at least one singular and one invertible matrix. We provide an explicit formula for the unique stationary measure associated to such cocycles and establish a Furstenberg-type formula characterizing the Lyapunov exponent. Using the spectral properties of the corresponding Markov operator and a parameter elimination argument, we prove that Lebesgue almost every cocycle in this space satisfies large deviations estimates and a central limit theorem. |
| title | Random 2D linear cocycles II: statistical properties |
| topic | Dynamical Systems Mathematical Physics 37A30 |
| url | https://arxiv.org/abs/2505.00146 |