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| HAL: inria-00552081, version 1 |
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| Intriguing Patterns in the Roots of the Derivatives of some Random Polynomials |
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| André Galligo 1, 2 |
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| (2010-12-20) |
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| Our observations show that the sets of real (respectively complex) roots of the derivatives of some classical families of random polynomials admit a rich variety of patterns looking like discretized curves. To bring out the shapes of the suggested curves, we introduce an original use of fractional derivatives. Then we set several conjectures and outline a strategy to explain the presented phenomena. This strategy is based on asymptotic geometric properties of the corresponding complex critical points sets. |
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| 1: | Laboratoire Jean Alexandre Dieudonné (JAD) |
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CNRS : UMR6621 – Université de Nice Sophia Antipolis (UNS) |
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| 2: | GALAAD (INRIA Sophia Antipolis) |
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INRIA – CNRS : UMR6621 – Université de Nice Sophia Antipolis (UNS) |
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| Domain | : | Mathematics/Differential Geometry |
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| Random polynomials – Roots of polynomials – Fractional derivatives – Critical points – Pattern. |
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| Attached file list to this document: | |||||
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| inria-00552081, version 1 | |
| http://hal.inria.fr/inria-00552081 | |
| oai:hal.inria.fr:inria-00552081 | |
| From: André Galligo | |
| Submitted on: Wednesday, 5 January 2011 14:00:57 | |
| Updated on: Wednesday, 5 January 2011 14:31:44 | |
