Non-commutative Law of iterated logarithm
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918148746248192 |
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| author | Panja, Sourav Ricard, Éric Saha, Diptesh |
| author_facet | Panja, Sourav Ricard, Éric Saha, Diptesh |
| contents | We prove optimal non-commutative analogues of the classical Law of Iterated Logarithm (LIL) for both martingales and sequences of independent (non-commutative) random variables. The classical martingale version was established by Stout [Sto70b] and the independent case by Hartman-Wintner [HW41]. Our approach relies on a key exponential inequality essentially due to Randrianantoanina [Ran24] that improves that from Junge and Zeng [JZ15]. It allows to derive an optimal non-commutative Stout-type LIL just as in [Zen15], from that martingale result we then deduce a non-commutative Hartman-Wintner type LIL for independent sequences of random variables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_22037 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-commutative Law of iterated logarithm Panja, Sourav Ricard, Éric Saha, Diptesh Operator Algebras Functional Analysis Probability 46L53, 46L55 We prove optimal non-commutative analogues of the classical Law of Iterated Logarithm (LIL) for both martingales and sequences of independent (non-commutative) random variables. The classical martingale version was established by Stout [Sto70b] and the independent case by Hartman-Wintner [HW41]. Our approach relies on a key exponential inequality essentially due to Randrianantoanina [Ran24] that improves that from Junge and Zeng [JZ15]. It allows to derive an optimal non-commutative Stout-type LIL just as in [Zen15], from that martingale result we then deduce a non-commutative Hartman-Wintner type LIL for independent sequences of random variables. |
| title | Non-commutative Law of iterated logarithm |
| topic | Operator Algebras Functional Analysis Probability 46L53, 46L55 |
| url | https://arxiv.org/abs/2509.22037 |