ツリーとネットワークの確率論<br>Probability on Trees and Networks

個数:1
紙書籍版価格
¥15,764
  • 電子書籍
  • ポイントキャンペーン

ツリーとネットワークの確率論
Probability on Trees and Networks

  • 著者名:Lyons, Russell/Peres, Yuval
  • 価格 ¥9,009 (本体¥8,190)
  • Cambridge University Press(2017/01/20発売)
  • 3月の締めくくり!Kinoppy 電子書籍・電子洋書 全点ポイント30倍キャンペーン(~3/31)
  • ポイント 2,430pt (実際に付与されるポイントはご注文内容確認画面でご確認下さい)
  • 言語:ENG
  • ISBN:9781107160156
  • eISBN:9781316784372

ファイル: /

Description

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.

Table of Contents

1. Some highlights; 2. Random walks and electric networks; 3. Special networks; 4. Uniform spanning trees; 5. Branching processes, second moments, and percolation; 6. Isoperimetric inequalities; 7. Percolation on transitive graphs; 8. The mass-transport technique and percolation; 9. Infinite electrical networks and Dirichlet functions; 10. Uniform spanning forests; 11. Minimal spanning forests; 12. Limit theorems for Galton–Watson processes; 13. Escape rate of random walks and embeddings; 14. Random walks on groups and Poisson boundaries; 15. Hausdorff dimension; 16. Capacity and stochastic processes; 17. Random walks on Galton–Watson trees.