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Infinite stable Boltzmann
planar maps are subdiffusive
Nicolas Curien and Cyril Marzouk |
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Vol. 2 (2021), No. 1, 1–26
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DOI: 10.2140/pmp.2021.2.1
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Abstract |
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The infinite discrete stable Boltzmann maps are generalisations of the well-known uniform infinite planar quadrangulation in the case where large degree faces are allowed. We show that the simple random walk on these random lattices is always subdiffusive with exponent less than . Our method is based on stationarity and geometric estimates obtained via the peeling process which are of individual interest. |
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Keywords
random maps, random walk, subdiffusivity, anomalous
diffusion, peeling
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Mathematical Subject Classification 2010
Primary: 05C81, 60D05
Secondary: 05C80, 60G10, 82B41
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Milestones
Received: 29 October 2019
Revised: 28 August 2020
Accepted: 12 October 2020
Published: 16 March 2021
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Authors |
| Nicolas Curien | |
| Département de Mathématique Université Paris–Saclay Faculté des Sciences d’Orsay Orsay France |
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| Cyril Marzouk | |
| Centre de Mathématiques
Appliquées École Polytechnique Palaiseau France |
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