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arXiv · 2509.06930

Obstructions to the regularity of the Lyapunov exponents for non-compact random Schr\"odinger cocycles

Pedro Duarte·Tomé Graxinha
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Abstract

In this paper, we present a class of random Schr\"odinger 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, H\"older continuity of the Lyapunov exponent requires an exponential moment condition.

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Pedro Duarte, Tomé Graxinha. 2025-09-08. Obstructions to the regularity of the Lyapunov exponents for non-compact random Schr\"odinger cocycles. https://arxiv.org/abs/2509.06930

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