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Free probability and random matrices

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arxiv 1404.3393 v1 pith:PX5W46MD submitted 2014-04-13 math.OA math.PR

classification math.OAmath.PR
keywords matricesrandomfreeprobabilityaddressalgebrasallowsasymptotic
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The concept of freeness was introduced by Voiculescu in the context of operator algebras. Later it was observed that it is also relevant for large random matrices. We will show how the combination of various free probability results with a linearization trick allows to address successfully the problem of determining the asymptotic eigenvalue distribution of general selfadjoint polynomials in independent random matrices.

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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. Correlation flow governs learning at criticality

    cs.LG 2026-08 conditional novelty 7.0 of 10

    At critical initialization, the infinite-depth neural tangent kernel converges to the fixed-point output correlation matrix divided by an activation-dependent constant, making learning dynamics equivalent to correlati...

  2. Random matrix perspective on probabilistic error cancellation

    quant-ph 2025-12 conditional novelty 6.0 of 10

    Denoiser channels in probabilistic error cancellation inherit their complex spectra from random Lindblad operators; local noise creates a hierarchy of decay timescales.

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