Matches in SemOpenAlex for { <https://semopenalex.org/work/W2894472289> ?p ?o ?g. }
Showing items 1 to 89 of
89
with 100 items per page.
- W2894472289 abstract "This paper contributes to the current studies on regularity properties of noncommutative distributions in free probability theory. More precisely, we consider evaluations of selfadjoint noncommutative polynomials in noncommutative random variables that have finite non-microstates free Fisher information, highlighting the special case of Lipschitz conjugate variables. For the first time in this generality, it is shown that the analytic distributions of those evaluations have Holder continuous cumulative distribution functions with an explicit Holder exponent that depends only on the degree of the considered polynomial. For linear polynomials, we reach in the case of finite non-microstates free Fisher information the optimal Holder exponent $frac{2}{3}$, and get Lipschitz continuity in the case of Lipschitz conjugate variables. In particular, our results guarantee that such polynomial evaluations have finite logarithmic energy and thus finite (non-microstates) free entropy, which partially settles a conjecture of Charlesworth and Shlyakhtenko [CS16]. We further provide a very general criterion that gives for weak approximations of measures having Holder continuous cumulative distribution functions explicit rates of convergence in terms of the Kolmogorov distance. Finally, we combine these results to study the asymptotic eigenvalue distributions of polynomials in GUEs or matrices with more general Gibbs laws. For Gibbs laws, this extends the corresponding result obtained in [GS09] from convergence in distribution to convergence in Kolmogorov distance; in the GUE case, we even provide explicit rates, which quantify results of [HT05,HST06] in terms of the Kolmogorov distance." @default.
- W2894472289 created "2018-10-05" @default.
- W2894472289 creator A5072148590 @default.
- W2894472289 creator A5083475624 @default.
- W2894472289 date "2018-09-28" @default.
- W2894472289 modified "2023-09-24" @default.
- W2894472289 title "Holder Continuity of Cumulative Distribution Functions for Noncommutative Polynomials under Finite Free Fisher Information" @default.
- W2894472289 cites W1586554030 @default.
- W2894472289 cites W1884490694 @default.
- W2894472289 cites W1989292836 @default.
- W2894472289 cites W1999830310 @default.
- W2894472289 cites W2013193877 @default.
- W2894472289 cites W2019129224 @default.
- W2894472289 cites W2019667538 @default.
- W2894472289 cites W2021217937 @default.
- W2894472289 cites W2022811481 @default.
- W2894472289 cites W2026938829 @default.
- W2894472289 cites W2034798756 @default.
- W2894472289 cites W2043256123 @default.
- W2894472289 cites W2051302879 @default.
- W2894472289 cites W2067963206 @default.
- W2894472289 cites W2075136665 @default.
- W2894472289 cites W2075252008 @default.
- W2894472289 cites W2127737388 @default.
- W2894472289 cites W2133313073 @default.
- W2894472289 cites W2154528415 @default.
- W2894472289 cites W2164746035 @default.
- W2894472289 cites W2202388696 @default.
- W2894472289 cites W2351657481 @default.
- W2894472289 cites W2487893106 @default.
- W2894472289 cites W2591821495 @default.
- W2894472289 cites W2798620122 @default.
- W2894472289 cites W2802234256 @default.
- W2894472289 cites W2962980630 @default.
- W2894472289 cites W2963003540 @default.
- W2894472289 cites W2963493594 @default.
- W2894472289 cites W3100713965 @default.
- W2894472289 doi "https://doi.org/10.48550/arxiv.1809.11153" @default.
- W2894472289 hasPublicationYear "2018" @default.
- W2894472289 type Work @default.
- W2894472289 sameAs 2894472289 @default.
- W2894472289 citedByCount "4" @default.
- W2894472289 countsByYear W28944722892018 @default.
- W2894472289 countsByYear W28944722892019 @default.
- W2894472289 countsByYear W28944722892021 @default.
- W2894472289 crossrefType "posted-content" @default.
- W2894472289 hasAuthorship W2894472289A5072148590 @default.
- W2894472289 hasAuthorship W2894472289A5083475624 @default.
- W2894472289 hasBestOaLocation W28944722891 @default.
- W2894472289 hasConcept C105795698 @default.
- W2894472289 hasConcept C122123141 @default.
- W2894472289 hasConcept C134306372 @default.
- W2894472289 hasConcept C138885662 @default.
- W2894472289 hasConcept C202444582 @default.
- W2894472289 hasConcept C22324862 @default.
- W2894472289 hasConcept C2780388253 @default.
- W2894472289 hasConcept C33923547 @default.
- W2894472289 hasConcept C41895202 @default.
- W2894472289 hasConcept C68797384 @default.
- W2894472289 hasConcept C90119067 @default.
- W2894472289 hasConceptScore W2894472289C105795698 @default.
- W2894472289 hasConceptScore W2894472289C122123141 @default.
- W2894472289 hasConceptScore W2894472289C134306372 @default.
- W2894472289 hasConceptScore W2894472289C138885662 @default.
- W2894472289 hasConceptScore W2894472289C202444582 @default.
- W2894472289 hasConceptScore W2894472289C22324862 @default.
- W2894472289 hasConceptScore W2894472289C2780388253 @default.
- W2894472289 hasConceptScore W2894472289C33923547 @default.
- W2894472289 hasConceptScore W2894472289C41895202 @default.
- W2894472289 hasConceptScore W2894472289C68797384 @default.
- W2894472289 hasConceptScore W2894472289C90119067 @default.
- W2894472289 hasLocation W28944722891 @default.
- W2894472289 hasLocation W28944722892 @default.
- W2894472289 hasOpenAccess W2894472289 @default.
- W2894472289 hasPrimaryLocation W28944722891 @default.
- W2894472289 hasRelatedWork W1995723465 @default.
- W2894472289 hasRelatedWork W2031889345 @default.
- W2894472289 hasRelatedWork W2039342738 @default.
- W2894472289 hasRelatedWork W2078854592 @default.
- W2894472289 hasRelatedWork W2319787826 @default.
- W2894472289 hasRelatedWork W2963108456 @default.
- W2894472289 hasRelatedWork W3084333948 @default.
- W2894472289 hasRelatedWork W4206722294 @default.
- W2894472289 hasRelatedWork W4248060259 @default.
- W2894472289 hasRelatedWork W954675015 @default.
- W2894472289 isParatext "false" @default.
- W2894472289 isRetracted "false" @default.
- W2894472289 magId "2894472289" @default.
- W2894472289 workType "article" @default.