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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


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


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.


Applications to Other Wh-Fronting Languages, Pied-Piping, and Intervention Effects

Seth Cable

in The Grammar of Q: Q-Particles, Wh-Movement, and Pied-Piping

Published in print:
2010
Published Online:
September 2010
ISBN:
9780195392265
eISBN:
9780199866526
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195392265.003.0004
Subject:
Linguistics, Syntax and Morphology

This chapter begins the argument that the ‘Q-based’ account should be extended to all other wh-fronting languages. It first presents some general typological and learning-theoretic arguments. These ... More


Optimization

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/9780199548927.003.0014
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter demonstrates how a universal requirement for optimality leads to the complex structural organization of a network. It discusses a long-lasting criticism of the preferential concept and ... More


Percolation and network resilience

Mark Newman

in Networks

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198805090
eISBN:
9780191843235
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198805090.003.0015
Subject:
Physics, Theoretical, Computational, and Statistical Physics

A discussion of the site percolation process on networks and its application as a model of network resilience. The chapter starts with a description of the percolation process, in which nodes are ... More


ELECTRON MOBILITY IN DENSE HE GAS

A.F. Borghesani

in Ions and electrons in liquid helium

Published in print:
2007
Published Online:
January 2008
ISBN:
9780199213603
eISBN:
9780191707421
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213603.003.0027
Subject:
Physics, Condensed Matter Physics / Materials

Experiments on the mobility of electrons in dense helium gas elucidated how localized electron states develop when the gas density gas is increased. Up to 77 K, the density dependence of the mobility ... More


Fractured Porous Media

Pierre M. Adler, Jean-François Thovert, and Valeri V. Mourzenko

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199666515
eISBN:
9780191748639
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199666515.001.0001
Subject:
Physics, Condensed Matter Physics / Materials

This book aims to estimate the macroscopic properties of fractures, fracture networks and fractured porous media from easily measurable quantities. Attention is focused on geological media where ... More


HOPPING CONDUCTIVITY

V.F. Gantmakher

in Electrons and Disorder in Solids

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198567561
eISBN:
9780191718267
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567561.003.0004
Subject:
Physics, Condensed Matter Physics / Materials

This chapter is dedicated to electron transitions between localized states. After a description of the states with the help of localization radius and the general expression for the transition ... More


First Steps in Random Walks: From Tools to Applications

J. Klafter and I. M. Sokolov

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199234868
eISBN:
9780191775024
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199234868.001.0001
Subject:
Physics, Soft Matter / Biological Physics

The name “random walk” for a problem of a displacement of a point in a sequence of independent random steps was coined by Karl Pearson in 1905 in a question posed to readers of “Nature”. The same ... More


Percolation and network resilience: A discussion of one of the simplest of processes taking place on networks, percolation, and its use as a model of network resilience

M. E. J. Newman

in Networks: An Introduction

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199206650
eISBN:
9780191594175
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199206650.003.0016
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter examines one of the simplest network processes, which is percolation. This leads to an elegant theory concerning the robustness of networked systems to the failure of their components. ... More


Random systems

Hidetoshi Nishimori and Gerardo Ortiz

in Elements of Phase Transitions and Critical Phenomena

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199577224
eISBN:
9780191722943
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199577224.003.0008
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Real materials always contain randomness or disorder that cannot be expressed by idealized simple model systems. The present chapter studies the effects of randomness on phase transitions and ... More


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