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Pointwise modulus of continuity of the Lyapunov exponent and integrated density of states for analytic multi-frequency quasiperiodic $M(2, \mathbb{C})$ cocycles

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arxiv 2310.10472 v1 pith:CR7H54FD submitted 2023-10-16 math-ph math.DSmath.MP

Matthew Powell This is my paper · ORCID
classification math-phmath.DSmath.MP
keywords densityintegratedstatesanalyticcertaincocyclecocyclescontinuity
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It is known that the Lyapunov exponent for multifrequency analytic cocycles is weak-H\"older continuous in cocycle for certain Diophantine frequencies, and that this implies certain regularity of the integrated density of states in energy for Jacobi operators. In this paper, we establish the pointwise modulus of continuity in both cocycle and frequency and obtain analogous regularity of the integrated density of states in energy, potential, and frequency.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. eSapiens's DEREK Module: Deep Extraction & Reasoning Engine for Knowledge with LLMs

    cs.CL 2025-07 reject novelty 3.0 of 10

    An enterprise RAG module with 1000-token chunks, hybrid retrieval, and a verifier reports small retrieval gains and low hallucination, but several headline numbers conflict with its own appendix tables.

  2. eSapiens: A Platform for Secure and Auditable Retrieval-Augmented Generation

    cs.AI 2025-07 reject novelty 2.0 of 10

    The abstract promises benchmark wins for the eSapiens RAG platform, but the appendix tables do not contain those numbers and show higher hallucination rates than the baseline.

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