Recurrence of the plane Elephant random walk
We give a short proof of the recurrence of the two-dimensional elephant random walk in the diffusive regime. This was recently established by Qin (2023), but our proof mainly uses very rough comparison with the standard plane random walk. We hope that the method can be useful for other applications.
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| Format: | Article |
| Language: | English |
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Académie des sciences
2024-11-01
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| Series: | Comptes Rendus. Mathématique |
| Subjects: | |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.620/ |
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| author | Curien, Nicolas Laulin, Lucile |
| author_facet | Curien, Nicolas Laulin, Lucile |
| author_sort | Curien, Nicolas |
| collection | DOAJ |
| description | We give a short proof of the recurrence of the two-dimensional elephant random walk in the diffusive regime. This was recently established by Qin (2023), but our proof mainly uses very rough comparison with the standard plane random walk. We hope that the method can be useful for other applications. |
| format | Article |
| id | doaj-art-dc4f961a83e54bc3a039a2e0a65fa38d |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-dc4f961a83e54bc3a039a2e0a65fa38d2025-02-07T11:23:31ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-11-01362G101183118810.5802/crmath.62010.5802/crmath.620Recurrence of the plane Elephant random walkCurien, Nicolas0Laulin, Lucile1https://orcid.org/0000-0002-9330-1042Laboratoire de mathématiques d’Orsay – UMR CNRS 8628, Université Paris-Saclay, 91405 Orsay, FranceModal’X - UMR CNRS 9023, Université Paris Nanterre, 92000 Nanterre, FranceWe give a short proof of the recurrence of the two-dimensional elephant random walk in the diffusive regime. This was recently established by Qin (2023), but our proof mainly uses very rough comparison with the standard plane random walk. We hope that the method can be useful for other applications.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.620/Elephant random walkrecurrence of random walkmartingales |
| spellingShingle | Curien, Nicolas Laulin, Lucile Recurrence of the plane Elephant random walk Comptes Rendus. Mathématique Elephant random walk recurrence of random walk martingales |
| title | Recurrence of the plane Elephant random walk |
| title_full | Recurrence of the plane Elephant random walk |
| title_fullStr | Recurrence of the plane Elephant random walk |
| title_full_unstemmed | Recurrence of the plane Elephant random walk |
| title_short | Recurrence of the plane Elephant random walk |
| title_sort | recurrence of the plane elephant random walk |
| topic | Elephant random walk recurrence of random walk martingales |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.620/ |
| work_keys_str_mv | AT curiennicolas recurrenceoftheplaneelephantrandomwalk AT laulinlucile recurrenceoftheplaneelephantrandomwalk |