| 書目名稱 | Peeling Random Planar Maps | | 副標(biāo)題 | école d’été de Proba | | 編輯 | Nicolas Curien | | 視頻video | http://file.papertrans.cn/744/743301/743301.mp4 | | 概述 | The first book on probabilistic aspects of planar maps.Provides comprehensive coverage of the theory and includes open problems.Illustrated with numerous attractive figures | | 叢書名稱 | Lecture Notes in Mathematics | | 圖書封面 |  | | 描述 | 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 PhD students 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 | | 出版日期 | Book 2023 | | 關(guān)鍵詞 | Graph Theory; Planar Maps; Combinatorics; Markov Property; Scaling Limits; Stable Processes; Combinatorial | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-031-36854-7 | | isbn_softcover | 978-3-031-36853-0 | | isbn_ebook | 978-3-031-36854-7Series ISSN 0075-8434 Series E-ISSN 1617-9692 | | issn_series | 0075-8434 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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