Exact asymptotics in a mean field model with random potential
type: Item
instance of: scholarly article
title: Exact asymptotics in a mean field model with random potential
zbMATH Open document ID: 0677.60105
DOI: 10.1007/BF01474644
author: Klaus Fleischmann
author: S. Molchanov
publication date: 1990-01-01T00:00:00Z
review text: For a mean field operator with a random potential, asymptotic properties of the eigenvalues and eigenfunctions are studied and applied to investigate the long term behavior of the solutions of a corresponding large system of differential equations. The total mass of the system is approximately concentrated in the record point of the random potential (complete localization). A more detailed inspection of the peaks shows that there is a phase transition: Only in the case of a moderate increase of time relatively to the growth of the space size the model behaves similarly as the system without ``diffusion''. But also in the non- moderate case the asymptotic height of peaks can exactly be described.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 4109812
zbMATH Keywords: mean field operator with a random potential
zbMATH Keywords: random potential
zbMATH Keywords: phase transition
zbMATH Keywords: asymptotic height of peaks
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01474644
OpenAlex ID: W1991990862
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
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description: scientific article; zbMATH DE number 4109812