Peeling Random Planar Maps École d’Été de Probabilités de Saint-Flour XLIX – 2019 /
These Lecture Notes provide an introduction to the study of those discrete surfaces which are obtained by randomly gluing polygons along their sides in a plane. The focus is on the geometry of such random planar maps (diameter, volume growth, scaling and local limits...) as well as the behavior of s...
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Springer Nature Switzerland : Imprint: Springer,
2023.
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| Izdaja: | 1st ed. 2023. |
| Serija: | École d'Été de Probabilités de Saint-Flour ;
2335 |
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| Online dostop: | https://doi.org/10.1007/978-3-031-36854-7 |
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| 100 | 1 | |a Curien, Nicolas. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Peeling Random Planar Maps |h [electronic resource] : |b École d’Été de Probabilités de Saint-Flour XLIX – 2019 / |c by Nicolas Curien. |
| 250 | |a 1st ed. 2023. | ||
| 264 | 1 | |a Cham : |b Springer Nature Switzerland : |b Imprint: Springer, |c 2023. | |
| 300 | |a 1 online resource (XVIII, 286 p. 120 illus.). |b 98 illus. in color. | ||
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| 490 | 1 | |a École d'Été de Probabilités de Saint-Flour ; |v 2335 | |
| 520 | |a These Lecture Notes provide an introduction to the study of those discrete surfaces which are obtained by randomly gluing polygons along their sides in a plane. The focus is on the geometry of such random planar maps (diameter, volume growth, scaling and local limits...) as well as the behavior of statistical mechanics models on them (percolation, simple random walks, self-avoiding random walks...). A “Markovian” approach is adopted to explore these random discrete surfaces, which is then related to the analogous one-dimensional random walk processes. This technique, known as "peeling exploration" in the literature, can be seen as a generalization of the well-known coding processes for random trees (e.g. breadth first or depth first search). It is revealed that different types of Markovian explorations can yield different types of information about a surface. Based on an École d'Été de Probabilités de Saint-Flour course delivered by the author in 2019, the book is aimed at PhDstudents and researchers interested in graph theory, combinatorial probability and geometry. Featuring open problems and a wealth of interesting figures, it is the first book to be published on the theory of random planar maps. | ||
| 532 | 8 | |a Accessibility summary: This PDF does Not fully comply with PDF/UA standards but does include limited screen reader support, descriptions for Non-text content (such as images and graphs), bookmarks for easy navigation, and searchable, selectable text. Users of assistive technologies may experience difficulty navigating or interpreting content in this document. We recognise the importance of accessibility and welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us via https://www.springernature.com/gp/info/accessibility | |
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| 588 | |a Print version record. | ||
| 650 | 0 | |a Probabilities. | |
| 650 | 0 | |a Graph theory. | |
| 650 | 0 | |a Geometry. | |
| 650 | 0 | |a Stochastic processes. | |
| 650 | 1 | 4 | |a Graph Theory in Probability. |
| 650 | 2 | 4 | |a Geometry. |
| 650 | 2 | 4 | |a Probability Theory. |
| 650 | 2 | 4 | |a Stochastic Processes. |
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| 776 | 0 | 8 | |i Printed edition: |z 9783031368530 |
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| 830 | 0 | |a École d'Été de Probabilités de Saint-Flour ; |v 2335 | |
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