Mean-field interaction of Brownian occupation measures. I: Uniform tube property of the Coulomb functional
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 2199 | |
dc.contributor.author | König, Wolfgang | |
dc.contributor.author | Mukherjee, Chiranjib | |
dc.date.accessioned | 2016-12-13T10:46:55Z | |
dc.date.available | 2019-06-28T08:01:55Z | |
dc.date.issued | 2015 | |
dc.description.abstract | In this paper, we study a transformed path measure that arises from a mean-field type interaction of a three dimensional Brownian motion in a Coulomb potential. Under the influence of such a transformed measure, the large-t behavior of the normalized occupation measures, denoted by Lt, is of high interest. This is intimately connected to the well-known polaron problem from statistical mechanics and a full understanding of the behavior of Lt under the aforementioned transformation is crucial for the analysis of the polaron path measure under ‘strong coupling’ , its effective mass and justification of mean-field approximations. For physical relevance of this model, we refer to [S86]. Some mathematically rigorous research in this direction began in the 1980s with the analysis of the partition function of Donsker and Varadhan ([DV83-P]), but it was not until recently that a new technique was developed [MV14] for handling the actual path measures, and the main results the present paper, besides being interesting on their own, make determinant contribution towards a deeper analysis and a full identification of the limiting distribution of Lt under the transformed path measure. | eng |
dc.description.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 2198-5855 | |
dc.identifier.uri | https://doi.org/10.34657/2644 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/1618 | |
dc.language.iso | eng | eng |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | eng |
dc.relation.issn | 0946-8633 | eng |
dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
dc.subject.ddc | 510 | eng |
dc.subject.other | Gibbs measures | eng |
dc.subject.other | interacting Brownian motions | eng |
dc.subject.other | Coulomb functional | eng |
dc.subject.other | polaron problem | eng |
dc.title | Mean-field interaction of Brownian occupation measures. I: Uniform tube property of the Coulomb functional | eng |
dc.type | Report | eng |
dc.type | Text | eng |
tib.accessRights | openAccess | eng |
wgl.contributor | WIAS | eng |
wgl.subject | Mathematik | eng |
wgl.type | Report / Forschungsbericht / Arbeitspapier | eng |
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