arXiv subjects

El Hadji Yaya Tall

Publications and source records attributed to El Hadji Yaya Tall.

3 recordsLinked to original sources

arXiv2026

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

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.

math.DS↗

arXiv2026

Log-Höder continuity at zero Lyapunov gap for finite state Markov $GL(2)$-cocycles

We prove that the extremal Lyapunov exponents of finite-state Markov $\mathrm{GL}(2,\mathbb{R})$-cocycles are pointwise log-Hölder continuous, jointly in the cocycle matrices and the transition kernel, at every parameter $(A,P)$ satisfying $λ_+(A,P)=λ_-(A,P)$. Perturbations are taken within a fixed transition graph. The main new ingredient is a Markov perpetuity estimate for the nonsplit triangular case, obtained through a martingale--coboundary decomposition. In the conformal case, the exponent $1/2$ in the logarithmic modulus can be replaced by $1$.

math.DS↗

arXiv2021

Analyticity of the Lyapunov exponents of random products of quasi-periodic cocycles

We show that the top Lyapunov exponent $λ_+(p)$ , $p = (p_1, \cdots, p_N)$ with $p_i >0$ for each $i$, associated with a random product of quasi-periodic cocycles depends real analytically on the transition probabilities $p$ whenever $λ_+(p)$ is simple. Moreover if the spectrum at $p$ is simple (all Lyapunov exponents having multiplicity one ) then all Lyapunov exponents depend real analytically on $p$.

math.DS↗