The Brownian web, the Brownian net, and their universality

Kód výsledku v IS VaVaI

RIV/67985556:_____/16:00476050 - isvavai.cz

Výsledek na webu

http://dx.doi.org/10.1017/9781316403877.007

DOI - Digital Object Identifier

10.1017/9781316403877.007

Jazyk výsledku

angličtina

Název v původním jazyce

The Brownian web, the Brownian net, and their universality

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

The Brownian web, the Brownian net, and their universality

Popis výsledku anglicky

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.

Druh

C - Kapitola v odborné knize

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

GA15-08819S: Stochastické procesy v nekonečně rozměrných prostorech

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2016

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název knihy nebo sborníku

Advances in Disordered Systems, Random Processes and Some Applications

ISBN

9781107124103

Počet stran výsledku

99

Strana od-do

270-368

Počet stran knihy

380

Název nakladatele

Cambridge University Press

Místo vydání

Cambridge

Kód UT WoS kapitoly

—