Hölder regularity of the top Lyapunov exponent for random matrix products with low-dimensional equator

Ana Cristina Barreto; Adriana Sánchez; El Hadji Yaya Tall; Marcelo Viana

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arXiv · 2610.17153

Hölder regularity of the top Lyapunov exponent for random matrix products with low-dimensional equator

Ana Cristina Barreto·Adriana Sánchez·El Hadji Yaya Tall·Marcelo Viana

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Abstract

We investigate the regularity of Lyapunov exponents for products of random invertible matrices of arbitrary dimension $d\ge 2$. We prove that the top Lyapunov exponent is pointwise Hölder continuous with respect to the Wasserstein-Hausdorff distance in the space of probability measures with compact support, in the case where this exponent is simple and the equator has dimension equal to or less than one.

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Ana Cristina Barreto, Adriana Sánchez, El Hadji Yaya Tall, Marcelo Viana. 2026-10-12. Hölder regularity of the top Lyapunov exponent for random matrix products with low-dimensional equator. https://arxiv.org/abs/2610.17153

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