Peeling Random Planar Maps: École d'Été de Probabilités de Saint-Flour XLIX - 2019

Curien, Nicolas

  • 出版商: Springer
  • 出版日期: 2023-11-21
  • 售價: $2,650
  • 貴賓價: 9.5$2,518
  • 語言: 英文
  • 頁數: 286
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3031368533
  • ISBN-13: 9783031368530
  • 海外代購書籍(需單獨結帳)

相關主題

商品描述

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 random planar maps.

商品描述(中文翻譯)

這些講義介紹了一種在平面上通過隨機地將多邊形沿著邊緣黏合而獲得的離散曲面的研究。重點在於這些隨機平面圖的幾何特性(直徑、體積增長、縮放和局部極限...)以及統計力學模型在其上的行為(滲透、簡單隨機行走、自避隨機行走...)。

本書採用了一種「馬可夫」方法來探索這些隨機離散曲面,並將其與類似的一維隨機行走過程相關聯。這種在文獻中被稱為「剝皮探索」的技術可以看作是對隨機樹的編碼過程(例如廣度優先搜索或深度優先搜索)的一種推廣。研究發現,不同類型的馬可夫探索可以提供關於曲面的不同類型的信息。

本書基於作者於2019年在聖弗洛爾概率夏季學校上的課程,針對對圖論、組合概率和幾何學感興趣的博士生和研究人員。書中包含開放問題和豐富的有趣圖表,是第一本關於隨機平面圖理論的出版物。

作者簡介

Nicolas Curien has been a Professor at Université Paris-Saclay since 2014. He works on random geometry in a broad sense.

作者簡介(中文翻譯)

Nicolas Curien自2014年起擔任巴黎-索克萊大學的教授。他的研究範圍涵蓋了廣義的隨機幾何學。