Probability on Trees and Networks (Hardcover)

Russell Lyons, Yuval Peres

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商品描述

Starting around the late 1950s, several research communities began relating the geometry of graphs to stochastic processes on these graphs. This book, twenty years in the making, ties together research in the field, encompassing work on percolation, isoperimetric inequalities, eigenvalues, transition probabilities, and random walks. Written by two leading researchers, the text emphasizes intuition, while giving complete proofs and more than 850 exercises. Many recent developments, in which the authors have played a leading role, are discussed, including percolation on trees and Cayley graphs, uniform spanning forests, the mass-transport technique, and connections on random walks on graphs to embedding in Hilbert space. This state-of-the-art account of probability on networks will be indispensable for graduate students and researchers alike.

商品描述(中文翻譯)

從1950年代末期開始,幾個研究社群開始將圖形的幾何結構與這些圖形上的隨機過程相關聯。這本書花了二十年的時間,將這個領域的研究結合在一起,包括對滲透、等周不等式、特徵值、轉移機率和隨機遊走的工作。由兩位領先的研究者撰寫,本書強調直觀,同時提供完整的證明和超過850個練習題。書中討論了許多最近的發展,其中作者發揮了領導作用,包括樹和Cayley圖上的滲透、均勻生成森林、質量傳輸技術,以及圖形上的隨機遊走與Hilbert空間嵌入的關聯。這本關於網絡上的概率的最新研究將對研究生和研究人員都是不可或缺的。