Pith. sign in

REVIEW 3 cited by

Continuity of the Lyapunov exponents of random matrix products

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2305.06009 v1 pith:NR2FGWBF submitted 2023-05-10 math.DS

Artur Avila , Alex Eskin , Marcelo Viana This is my paper · ORCID
classification math.DS
keywords exponentslyapunovmatrixrandomcontinuouslydistributionprobabilityproducts
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We prove that the Lyapunov exponents of random products in a (real or complex) matrix group depends continuously on the matrix coefficients and probability weights. More generally, the Lyapunov exponents of the random product defined by any compactly supported probability distribution on $GL(d)$ vary continuously with the distribution, in a natural topology corresponding to weak$^*$-closeness of the distributions and Hausdorff-closeness of their supports.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 3 Pith papers

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

  1. Dimers with layered disorder

    math.PR 2025-07 conditional novelty 8.0 of 10

    Layered disorder creates an essential singularity in the dimer free energy and modifies the liquid-gas critical exponent continuously.

  2. Analyticity of Lyapunov Exponents for Mixed Markov Quasi-Periodic Cocycles

    math.DS 2026-08 conditional novelty 6.0 of 10

    The top Lyapunov exponent of a primitive Markov quasi-periodic cocycle with simple top spectrum has a holomorphic extension in a complex neighborhood of the transition matrix.

  3. Gaussian Universality of Products Over Split Reductive Groups and the Satake Isomorphism

    math.PR 2025-02 conditional novelty 6.0 of 10

    For products of bi-invariant random matrices over non-archimedean fields, singular numbers obey an SLLN and CLT with limits given by the corners, extending known type-A/type-C results to all split reductive groups.

Pith tools