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This is a Quantitative Study study.

October 12, 2025Open Access

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

Key Points

The presence of certain finite moment conditions is essential for establishing continuity of the lyapunov exponent.
Hölder continuity specifically requires an exponential moment condition to be satisfied.
Random cocycles with non-compact support exhibit unique characteristics impacting lyapunov exponents.
Understanding these conditions can enhance mathematical approaches in random systems.

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.

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Cite This Study

Duarte et al. (Mon,) studied this question.

synapsesocial.com/papers/68ec1be02b8fa9b2b78ad2f0 https://doi.org/https://doi.org/10.48550/arxiv.2509.06930

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