## 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

## Very Fast Oscillations

*Roger D. Roger and Miles A. Whittington*

### in Cortical Oscillations in Health and Disease

- Published in print:
- 2010
- Published Online:
- May 2010
- ISBN:
- 9780195342796
- eISBN:
- 9780199776276
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195342796.003.0010
- Subject:
- Neuroscience, Molecular and Cellular Systems, Development

VFO occurs in in vitro models when chemical receptors are blocked. In particular, VFO does not require GABAA receptors, even though interneurons fire at high rates during in vivo very fast ... More

## Percolation and epidemics

*Sergey N. Dorogovtsev*

### in Lectures on Complex Networks

- Published in print:
- 2010
- Published Online:
- May 2010
- ISBN:
- 9780199548927
- eISBN:
- 9780191720574
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199548927.003.0006
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter considers the organization of connected components in uncorrelated networks, in particular, the structure and size of a giant connected component. These properties are closely related to ... 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

## Information Percolation in OTC Markets

*Darrell Duffie*

### in Dark Markets: Asset Pricing and Information Transmission in Over-the-Counter Markets

- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691138961
- eISBN:
- 9781400840519
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691138961.003.0005
- Subject:
- Economics and Finance, Financial Economics

This chapter describes a simple model of the “percolation” of information of common interest through an over-the-counter market with many agents. It also includes an explicit solution for the ... 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