The Brownian web, the Brownian net, and their universality
Result description
The Brownian web is a collection of one-dimensional coalescing Brownian motions starting from everywhere in space and time, and the Brownian net is a generalization that also allows branching. They appear in the diffusive scaling limits of many one-dimensional interacting particle systems with branching and coalescence. This article gives an introduction to the Brownian web and net, and how they arise in the scaling limits of various one-dimensional models, focusing mainly on coalescing random walks and random walks in id. space-time random environments. We will also briefly survey models and results connected to the Brownian web and net, including alternative topologies, population genetic models, true self-repelling motion, planar aggregation, drainage networks, oriented percolation, black noise and critical percolation. Some open questions are discussed at the end.
Keywords
The result's identifiers
Result code in IS VaVaI
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
The Brownian web, the Brownian net, and their universality
Original language description
The Brownian web is a collection of one-dimensional coalescing Brownian motions starting from everywhere in space and time, and the Brownian net is a generalization that also allows branching. They appear in the diffusive scaling limits of many one-dimensional interacting particle systems with branching and coalescence. This article gives an introduction to the Brownian web and net, and how they arise in the scaling limits of various one-dimensional models, focusing mainly on coalescing random walks and random walks in id. space-time random environments. We will also briefly survey models and results connected to the Brownian web and net, including alternative topologies, population genetic models, true self-repelling motion, planar aggregation, drainage networks, oriented percolation, black noise and critical percolation. Some open questions are discussed at the end.
Czech name
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Czech description
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Classification
Type
C - Chapter in a specialist book
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
GA15-08819S: Stochastic Processes in Infinite Dimensional Spaces
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Book/collection name
Advances in Disordered Systems, Random Processes and Some Applications
ISBN
9781107124103
Number of pages of the result
99
Pages from-to
270-368
Number of pages of the book
380
Publisher name
Cambridge University Press
Place of publication
Cambridge
UT code for WoS chapter
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Basic information
Result type
C - Chapter in a specialist book
OECD FORD
Pure mathematics
Year of implementation
2016