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Planar Maps, Random Walks and Circle Packing: École d'Été de Probabilités de Saint-Flour XLVIII - 2018
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| Titel: | Planar Maps, Random Walks and Circle Packing: École d'Été de Probabilités de Saint-Flour XLVIII - 2018/ by Asaf Nachmias |
| Ausgabe: | 1st ed. 2020 |
| Format: | E-Book |
| Sprache: | Englisch |
| veröffentlicht: |
Cham
Springer
2020
|
| Gesamtaufnahme: |
École d'Été de Probabilités de Saint-Flour Springer eBooks Lecture notes in mathematics ; 2243 |
| Schlagwörter: | |
| Erscheint auch als: | Nachmias, Asaf, Planar maps, random walks and circle packing, Cham : Springer Open, 2020, xii, 118 Seiten |
| Quelle: | Verbunddaten SWB Lizenzfreie Online-Ressourcen |
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| contents | This open access book focuses on the interplay between random walks on planar maps and Koebe’s circle packing theorem. Further topics covered include electric networks, the He–Schramm theorem on infinite circle packings, uniform spanning trees of planar maps, local limits of finite planar maps and the almost sure recurrence of simple random walks on these limits. One of its main goals is to present a self-contained proof that the uniform infinite planar triangulation (UIPT) is almost surely recurrent. Full proofs of all statements are provided. A planar map is a graph that can be drawn in the plane without crossing edges, together with a specification of the cyclic ordering of the edges incident to each vertex. One widely applicable method of drawing planar graphs is given by Koebe’s circle packing theorem (1936). Various geometric properties of these drawings, such as existence of accumulation points and bounds on the radii, encode important probabilistic information, such as the recurrence/transience of simple random walks and connectivity of the uniform spanning forest. This deep connection is especially fruitful to the study of random planar maps. The book is aimed at researchers and graduate students in mathematics and is suitable for a single-semester course; only a basic knowledge of graduate level probability theory is assumed |
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| spelling | Nachmias, Asaf VerfasserIn (DE-588)1198720433 (DE-627)1680894102 aut, Planar Maps, Random Walks and Circle Packing École d'Été de Probabilités de Saint-Flour XLVIII - 2018 by Asaf Nachmias, 1st ed. 2020, Cham Springer 2020, 1 Online-Ressource (XII, 120 p. 36 illus., 8 illus. in color), Text txt rdacontent, Computermedien c rdamedia, Online-Ressource cr rdacarrier, Lecture Notes in Mathematics 2243, Springer eBook Collection, École d'Été de Probabilités de Saint-Flour 2018, Springer eBooks Mathematics and Statistics, Open Access, This open access book focuses on the interplay between random walks on planar maps and Koebe’s circle packing theorem. Further topics covered include electric networks, the He–Schramm theorem on infinite circle packings, uniform spanning trees of planar maps, local limits of finite planar maps and the almost sure recurrence of simple random walks on these limits. One of its main goals is to present a self-contained proof that the uniform infinite planar triangulation (UIPT) is almost surely recurrent. Full proofs of all statements are provided. A planar map is a graph that can be drawn in the plane without crossing edges, together with a specification of the cyclic ordering of the edges incident to each vertex. One widely applicable method of drawing planar graphs is given by Koebe’s circle packing theorem (1936). Various geometric properties of these drawings, such as existence of accumulation points and bounds on the radii, encode important probabilistic information, such as the recurrence/transience of simple random walks and connectivity of the uniform spanning forest. This deep connection is especially fruitful to the study of random planar maps. The book is aimed at researchers and graduate students in mathematics and is suitable for a single-semester course; only a basic knowledge of graduate level probability theory is assumed, Probability Theory and Stochastic Processes, Distribution (Probability theory, Geometry, Discrete mathematics., Probabilities., Mathematical physics., 9783030279677, Erscheint auch als Druck-Ausgabe Nachmias, Asaf Planar maps, random walks and circle packing Cham : Springer Open, 2020 xii, 118 Seiten (DE-627)1679125176 9783030279677, Lecture notes in mathematics 2243 2243 (DE-627)348584407 (DE-576)100800718 (DE-600)2079379-0 1617-9692 ns, https://doi.org/10.1007/978-3-030-27968-4 X:SPRINGER Resolving-System kostenfrei, https://doi.org/10.1007/978-3-030-27968-4 DE-14, DE-14 epn:3850968596 2021-02-10T13:03:24Z, https://doi.org/10.1007/978-3-030-27968-4 Online-Zugriff DE-15, DE-15 epn:3533061663 2019-10-31T10:24:49Z, https://doi.org/10.1007/978-3-030-27968-4 DE-Ch1, DE-Ch1 epn:3551103259 2019-11-28T16:33:27Z, DE-105 epn:3564738177 2019-12-13T16:46:08Z, DE-Zwi2 epn:3533061698 del:202301280133, https://doi.org/10.1007/978-3-030-27968-4 Zum Online-Dokument DE-Zi4, DE-Zi4 epn:4104248150 2023-07-24T09:45:55Z, DE-L189 epn:3533061701 2019-10-31T10:24:49Z, https://doi.org/10.1007/978-3-030-27968-4 LFER, LFER epn:3563540241 2019-12-05T00:00:00Z |
| spellingShingle | Nachmias, Asaf, Planar Maps, Random Walks and Circle Packing: École d'Été de Probabilités de Saint-Flour XLVIII - 2018, Lecture notes in mathematics, 2243, This open access book focuses on the interplay between random walks on planar maps and Koebe’s circle packing theorem. Further topics covered include electric networks, the He–Schramm theorem on infinite circle packings, uniform spanning trees of planar maps, local limits of finite planar maps and the almost sure recurrence of simple random walks on these limits. One of its main goals is to present a self-contained proof that the uniform infinite planar triangulation (UIPT) is almost surely recurrent. Full proofs of all statements are provided. A planar map is a graph that can be drawn in the plane without crossing edges, together with a specification of the cyclic ordering of the edges incident to each vertex. One widely applicable method of drawing planar graphs is given by Koebe’s circle packing theorem (1936). Various geometric properties of these drawings, such as existence of accumulation points and bounds on the radii, encode important probabilistic information, such as the recurrence/transience of simple random walks and connectivity of the uniform spanning forest. This deep connection is especially fruitful to the study of random planar maps. The book is aimed at researchers and graduate students in mathematics and is suitable for a single-semester course; only a basic knowledge of graduate level probability theory is assumed, Probability Theory and Stochastic Processes, Distribution (Probability theory, Geometry, Discrete mathematics., Probabilities., Mathematical physics. |
| title | Planar Maps, Random Walks and Circle Packing: École d'Été de Probabilités de Saint-Flour XLVIII - 2018 |
| title_auth | Planar Maps, Random Walks and Circle Packing École d'Été de Probabilités de Saint-Flour XLVIII - 2018 |
| title_full | Planar Maps, Random Walks and Circle Packing École d'Été de Probabilités de Saint-Flour XLVIII - 2018 by Asaf Nachmias |
| title_fullStr | Planar Maps, Random Walks and Circle Packing École d'Été de Probabilités de Saint-Flour XLVIII - 2018 by Asaf Nachmias |
| title_full_unstemmed | Planar Maps, Random Walks and Circle Packing École d'Été de Probabilités de Saint-Flour XLVIII - 2018 by Asaf Nachmias |
| title_in_hierarchy | 2243. Planar Maps, Random Walks and Circle Packing: École d'Été de Probabilités de Saint-Flour XLVIII - 2018 (2020) |
| title_short | Planar Maps, Random Walks and Circle Packing |
| title_sort | planar maps, random walks and circle packing école d'été de probabilités de saint-flour xlviii - 2018 |
| title_sub | École d'Été de Probabilités de Saint-Flour XLVIII - 2018 |
| title_unstemmed | Planar Maps, Random Walks and Circle Packing: École d'Été de Probabilités de Saint-Flour XLVIII - 2018 |
| topic | Probability Theory and Stochastic Processes, Distribution (Probability theory, Geometry, Discrete mathematics., Probabilities., Mathematical physics. |
| topic_facet | Probability Theory and Stochastic Processes, Distribution (Probability theory, Geometry, Discrete mathematics., Probabilities., Mathematical physics. |
| url | https://doi.org/10.1007/978-3-030-27968-4 |
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