Joint spectrum and large deviation principle for random matrix products
Probability
2017-02-23 v1 Dynamical Systems
Group Theory
Metric Geometry
Abstract
The aim of this note is to announce some results about the probabilistic and deterministic asymptotic properties of linear groups. The first one is the analogue, for norms of random matrix products, of the classical theorem of Cramer on large deviation principles (LDP) for sums of iid real random variables. In the second result, we introduce a limit set describing the asymptotic shape of the powers of a subset S of a semisimple linear Lie group G (e.g. SL(d;R)). This limit set has applications, among others, in the study of large deviations.
Cite
@article{arxiv.1702.06937,
title = {Joint spectrum and large deviation principle for random matrix products},
author = {Cagri Sert},
journal= {arXiv preprint arXiv:1702.06937},
year = {2017}
}
Comments
Research announcement, 7 pages, submitted to Comptes Rendus Mathematique