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The Matsumoto-Yor property in free probability via subordination and Boolean cumulants

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Marcin Świeca

Operator Algebras · Submitted 26 Sep 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We prove three characterizations of free-GIG and free Poisson distributions by freeness properties together with some assumptions about conditional moments.

how it is stated · asserted 1.00 read the record →

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arXiv ID2109.12545 (version 1)
Pith IDN47IYHA2, Pith's permanent record of this paper and its review
CitationMarcin \'Swieca. "The Matsumoto-Yor property in free probability via subordination and Boolean cumulants." arXiv:2109.12545 (2021). https://pith.science/paper/N47IYHA2
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,467 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.25 · compares with prior results 0.11 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We study the Matsumoto-Yor property in free probability. We prove three characterizations of free-GIG and free Poisson distributions by freeness properties together with some assumptions about conditional moments. Our main tools are subordination and Boolean cumulants. In particular, we establish a new connection between additive subordination function and Boolean cumulants.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We study the Matsumoto-Yor property in free probability. contribution 0.63 0.89 0.04 asserted 0.74
s1 We prove three characterizations of free-GIG and free Poisson distributions by freeness properties together with some assumptions about conditional moments. result 0.77 0.96 0.68 asserted 1.00
s2 Our main tools are subordination and Boolean cumulants. method 1.00 0.63 0.06 asserted 0.99
s3 In particular, we establish a new connection between additive subordination function and Boolean cumulants. result 0.62 0.95 0.26 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

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not examined
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  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We study the Matsumoto-Yor property in free probability. We prove three characterizations of free-GIG and free Poisson distributions by freeness properties together with some assumptions about conditional moments. Our main tools are subordination and Boolean cumulants. In particular, we establish a new connection between additive subordination function and Boolean cumulants.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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