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Author : Olivier Bernardi
Publisher : American Mathematical Society
Page : 188 pages
File Size : 35,22 MB
Release : 2023-09-27
Category : Mathematics
ISBN : 1470466996
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Author : Erik Bates
Publisher : American Mathematical Society
Page : 110 pages
File Size : 10,60 MB
Release : 2024-02-01
Category : Mathematics
ISBN : 1470467917
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Author : Nicolas Curien
Publisher : Springer Nature
Page : 293 pages
File Size : 20,42 MB
Release : 2023-11-20
Category : Mathematics
ISBN : 3031368541
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 random planar maps.
Author : Mathias Pétréolle
Publisher : American Mathematical Society
Page : 166 pages
File Size : 36,65 MB
Release : 2024-01-19
Category : Mathematics
ISBN : 1470462680
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Author : Roberto Feola
Publisher : American Mathematical Society
Page : 170 pages
File Size : 18,99 MB
Release : 2024-04-17
Category : Mathematics
ISBN : 1470468778
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Author : Francisco Gancedo
Publisher : American Mathematical Society
Page : 100 pages
File Size : 23,5 MB
Release : 2024-01-26
Category : Mathematics
ISBN : 147046764X
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Author : Martin W. Liebeck
Publisher : American Mathematical Society
Page : 282 pages
File Size : 46,52 MB
Release : 2024-03-18
Category : Mathematics
ISBN : 1470469057
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Author : Alice Hedenlund
Publisher : American Mathematical Society
Page : 146 pages
File Size : 10,11 MB
Release : 2024-03-18
Category : Mathematics
ISBN : 1470468786
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Author : Tobias Rossmann
Publisher : American Mathematical Society
Page : 132 pages
File Size : 33,66 MB
Release : 2024-03-18
Category : Mathematics
ISBN : 1470468689
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Author : Jens Marklof
Publisher : American Mathematical Society
Page : 148 pages
File Size : 10,25 MB
Release : 2024-03-18
Category : Mathematics
ISBN : 1470468697
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