Diffusive clustering in an infinite system of hierarchically interacting diffusions
type: Item
instance of: scholarly article
title: Diffusive clustering in an infinite system of hierarchically interacting diffusions
zbMATH Open document ID: 0794.60107
DOI: 10.1007/BF01192837
author: Klaus Fleischmann
author: Andreas Greven
publication date: 1994-08-28T00:00:00Z
review text: We study a countable system of interacting diffusions on the interval [0,1], indexed by a hierarchical group. A particular choice of the interaction guarantees, we are in the diffusive clustering regime. This means clusters of components with values either close to 0 or close to 1 grow on various different scales. However, single components oscillate infinitely often between values close to 0 and close to 1 in such a way that they spend fraction one of their time together and close to the boundary. The processes in the whole class considered and starting with a shift-ergodic initial law have the same qualitative properties (universality).
reviewed by: Klaus Fleischmann
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60J60
zbMATH DE Number: 569028
zbMATH Keywords: weak interaction
zbMATH Keywords: clustering in time
zbMATH Keywords: interacting diffusions
zbMATH Keywords: shift- ergodic initial law
MaRDI profile type: Publication
cites work: Consolidation rates for two interacting systems in the plane
cites work: Q5524074
cites work: Q3976802
cites work: Ergodic theorems for infinite systems of locally interacting diffusions
cites work: Occupation time limit theorems for the voter model
cites work: Diffusive clustering in the two dimensional voter model
cites work: Mean Field Asymptotics for the Planar Stepping Stone Model
cites work: Hierarchical models of interacting diffusions: Multiple time scale phenomena, phase transition and pattern of cluster-formation
cites work: Q3138629
cites work: Some problems concerning the structure of random walk paths
cites work: Q3721531
cites work: Q5624436
cites work: Q4179614
cites work: A phase transition for the coupled branching process. I: The ergodic theory in the range of finite second moments
cites work: Q5185817
cites work: Ergodic theorems for coupled random walks and other systems with locally interacting components
cites work: Convergence to genetically uniform state in stepping stone models of population genetics
cites work: Isolation by distance in a hierarchically clustered population
cites work: An interacting system in population genetics
cites work: An interacting system in population genetics. II
cites work: Infinite dimensional stochastic differential equations and their applications
cites work: Line-of-descent and genealogical processes, and their applications in population genetics models
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 569028