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The Resource Voter model perturbations and reaction diffusion equations, J. Theodore Cox, Richard Durrett , Edwin A. Perkins

Voter model perturbations and reaction diffusion equations, J. Theodore Cox, Richard Durrett , Edwin A. Perkins

Label
Voter model perturbations and reaction diffusion equations
Title
Voter model perturbations and reaction diffusion equations
Statement of responsibility
J. Theodore Cox, Richard Durrett , Edwin A. Perkins
Creator
Contributor
Author
Publisher
Subject
Language
  • eng
  • fre
  • eng
Summary
  • "Keywords and phrases: Interacting particle systems, voter model, reaction diffusion equation, evolutionary game theory, Lotka-Volterra model"--Title page verso
  • "We consider particle systems that are perturbations of the voter model and show that when space and time are rescaled the system converges to a solution of a reaction diffusion equation in dimensions d[greater than or equal to]3. Combining this result with properties of the P.D.E., some methods arising from a low density super-Brownian limit theorem, and a block construction, we give general, and often asymptotically sharp, conditions for the existence of non-trivial stationary distributions, and for extinction of one type. As applications, we describe the phase diagrams of four systems when the parameters are close to the voter model: (i) a stochastic spatial Lotka-Volterra model of Neuhauser and Pacala, (ii) a model of the evolution of cooperation of Ohtsuki, Hauert, Lieberman, and Nowak, (iii) a continuous time version of the non-linear voter model of Molofsky, Durrett, Dushoff, Griffeath, and Levin, (iv) a voter model in which opinion changes are followed by an exponentially distributed latent period during which voters will not change again. The first application confirms a conjecture of Cox and Perkins ("Survival and coexistence in stochastic spatial Lotka-Volterra models", 2007) and the second confirms a conjecture of Ohtsuki et al. ("A simple rule for the evolution of cooperation on graphs and social networks", 2006) in the context of certain infinite graphs. An important feature of our general results is that they do not require the process to be attractive."--Page [4] of cover
Member of
Cataloging source
UKMGB
http://library.link/vocab/creatorName
Cox, J. T
Illustrations
illustrations
Index
no index present
Language note
Text in English; abstracts in English and French
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/relatedWorkOrContributorDate
  • 1951-
  • 1953-
http://library.link/vocab/relatedWorkOrContributorName
  • Durrett, Richard
  • Perkins, Edwin Arend
  • Société mathématique de France
Series statement
Astérisque;
Series volume
349
http://library.link/vocab/subjectName
  • Percolation (Statistical physics)
  • Stochastic processes
  • Reaction-diffusion equations
  • Perturbation (Mathematics)
  • Percolation (Statistical physics)
  • Stochastic processes
  • Reaction-diffusion equations
  • Perturbation (Mathematics)
Label
Voter model perturbations and reaction diffusion equations, J. Theodore Cox, Richard Durrett , Edwin A. Perkins
Instantiates
Publication
Note
"Publié avec le concours du Centre national de la recherche scientifique"--Title page
Bibliography note
  • Includes bibliographical references (pages 111-113)
  • Includes bibliographical references
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier.
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
Introduction and statement of results -- Construction, duality and coupling -- Proofs of theorems 1.2 and 1.3 -- Achieving low density -- Percolation results -- Existence of stationary distributions -- Extinction of the process
Control code
844871394
Dimensions
24 cm
Extent
vi, 113 pages
Isbn
9782856293553
Isbn Type
(paperback)
Media category
unmediated
Media MARC source
rdamedia.
Media type code
  • n
Other physical details
illustrations (black and white)
System control number
(OCoLC)844871394
Label
Voter model perturbations and reaction diffusion equations, J. Theodore Cox, Richard Durrett , Edwin A. Perkins
Publication
Note
"Publié avec le concours du Centre national de la recherche scientifique"--Title page
Bibliography note
  • Includes bibliographical references (pages 111-113)
  • Includes bibliographical references
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier.
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
Introduction and statement of results -- Construction, duality and coupling -- Proofs of theorems 1.2 and 1.3 -- Achieving low density -- Percolation results -- Existence of stationary distributions -- Extinction of the process
Control code
844871394
Dimensions
24 cm
Extent
vi, 113 pages
Isbn
9782856293553
Isbn Type
(paperback)
Media category
unmediated
Media MARC source
rdamedia.
Media type code
  • n
Other physical details
illustrations (black and white)
System control number
(OCoLC)844871394

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