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Random Geometric Graphs

Mathew Penrose

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198506263
eISBN:
9780191707858
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506263.001.0001
Subject:
Mathematics, Probability / Statistics

This book sets out a body of rigorous mathematical theory for finite graphs with nodes placed randomly in Euclidean d-space according to a common probability density, and edges added to connect ... More


New Perspectives in Stochastic Geometry

Wilfrid S. Kendall and Ilya Molchanov (eds)

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199232574
eISBN:
9780191716393
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199232574.001.0001
Subject:
Mathematics, Geometry / Topology

Stochastic geometry is a subject with roots stretching back at least 300 years, but one which has only been formed as an academic area in the last 50 years. It covers the study of random patterns, ... More


The Pleasures and Pains of Studying the Two-Type Richardson Model

Maria Deijfen and Olle Häggström

in Analysis and Stochastics of Growth Processes and Interface Models

Published in print:
2008
Published Online:
September 2008
ISBN:
9780199239252
eISBN:
9780191716911
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199239252.003.0002
Subject:
Mathematics, Probability / Statistics, Analysis

This chapter provides a survey of known results and open problems for the two-type Richardson model, which is a stochastic model for competition on a lattice. In its simplest formulation, the ... More


Applications of the Lace Expansion to Statistical-Mechanical Models

Akira Sakai

in Analysis and Stochastics of Growth Processes and Interface Models

Published in print:
2008
Published Online:
September 2008
ISBN:
9780199239252
eISBN:
9780191716911
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199239252.003.0006
Subject:
Mathematics, Probability / Statistics, Analysis

Synergetics is a common feature in interesting statistical-mechanical problems. One of the most important examples of synergetics is the emergence of a second-order phase transition and critical ... More


Combinatorics, Complexity, and Chance: A Tribute to Dominic Welsh

Geoffrey Grimmett and Colin McDiarmid (eds)

Published in print:
2007
Published Online:
September 2007
ISBN:
9780198571278
eISBN:
9780191718885
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198571278.001.0001
Subject:
Mathematics, Probability / Statistics

Professor Dominic Welsh has made significant contributions to the fields of combinatorics and discrete probability, including matroids, complexity, and percolation. He has taught, influenced, and ... More


PERCOLATIVE INGREDIENTS

Mathew Penrose

in Random Geometric Graphs

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198506263
eISBN:
9780191707858
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506263.003.0009
Subject:
Mathematics, Probability / Statistics

This chapter contains some known results on connectivity which are used later on. The notion of unicoherence of a simply-connected set is explained and extended to lattices. Peierls (counting) ... More


Stochastic Geometry and Telecommunications Networks

Sergei Zuyev

in New Perspectives in Stochastic Geometry

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199232574
eISBN:
9780191716393
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199232574.003.0016
Subject:
Mathematics, Geometry / Topology

Just as queueing theory revolutionized the study of circuit switched telephony in the twentieth century, stochastic geometry is gradually becoming a necessary theoretical tool for modelling and ... More


Percolation and Random Graphs

Remco van der Hofstad

in New Perspectives in Stochastic Geometry

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199232574
eISBN:
9780191716393
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199232574.003.0006
Subject:
Mathematics, Geometry / Topology

In this chapter, we define percolation and random graph models, and survey the features of these models.


The Plaid Model: (AMS-198)

Richard Evan Schwartz

Published in print:
2019
Published Online:
September 2019
ISBN:
9780691181387
eISBN:
9780691188997
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691181387.001.0001
Subject:
Mathematics, Educational Mathematics

Outer billiards provides a toy model for planetary motion and exhibits intricate and mysterious behavior even for seemingly simple examples. It is a dynamical system in which a particle in the plane ... More


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