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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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