Obstructions to the regularity of the Lyapunov exponents for non-compact random Schrödinger cocycles

2025/09/08 by Pedro Duarte, Duarte, Pedro, Tomé Graxinha +1 · 1 citation
Mathematics · Physics and Astronomy · #37A30 #37H15 #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2509.06930

openalex publication_date 2025/09/08 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

Abstract

In this paper, we present a class of random Schrödinger cocycles showing that, for random cocycles with non-compact support, the presence of certain finite moment conditions is essential for establishing a specific modulus of continuity of the Lyapunov exponent. In particular, Hölder continuity of the Lyapunov exponent requires an exponential moment condition.

Citations

• Hölder continuity of Lyapunov exponents for non-invertible and non-compact random cocycles
• Continuity of the Lyapunov exponents of random matrix products
• A dynamical Thouless formula
• Upper bound on the regularity of the Lyapunov exponent for random products of matrices
• On the abominable properties of the almost Mathieu operator with well approximated frequencies
• Schrödinger operators with dynamically defined potentials
• Holder Continuity of the Integrated Density of States for Quasi-Periodic Schrodinger Equations and Averages of Shifts of Subharmonic Functions
• Random matrix products and measures on projective spaces

Cited by

• The fibered rotation number

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• Continuity of the Lyapunov exponents of non-invertible random cocycles with constant rank
• Approximating Lyapunov exponents and stationary measures
• An abstract continuity theorem of the Lyapunov exponents