Probabilistic limit theorems induced by the zeros of polynomials
Abstract: Sequences of discrete random variables are studied whose probability generating functions are zero‐free in a sector of the complex plane around the positive real axis. Sharp bounds on the cumulants of all orders are stated, leading to Berry–Esseen bounds, moderate deviation results, concentration inequalities, and mod‐Gaussian convergence. In addition, an alternate proof of the cumulant bound with improved constants for a class of polynomials all of whose roots lie on the unit circle is provided. A variety of examples is discussed in detail.
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Bibliographic citation
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Probabilistic limit theorems induced by the zeros of polynomials ; day:26 ; month:12 ; year:2023 ; extent:21
Mathematische Nachrichten ; (26.12.2023) (gesamt 21)
- Creator
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Heerten, Nils
Sambale, Holger
Thäle, Christoph
- DOI
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10.1002/mana.202300109
- URN
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urn:nbn:de:101:1-2023122614062635859714
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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15.08.2025, 7:28 AM CEST
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Associated
- Heerten, Nils
- Sambale, Holger
- Thäle, Christoph
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