The Landau equation for Maxwellian molecules and the Brownian motion on SON(R)

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• dc.contributor.author Delarue, Françoisca
• dc.contributor.author Menozzi, Stéphaneca
• dc.contributor.author Nualart, Eulàliaca
• dc.date.accessioned 2018-04-18T08:30:59Z
• dc.date.available 2018-04-18T08:30:59Z
• dc.date.issued 2015
• dc.description.abstract In this paper we prove that the spatially homogeneous Landau equation for Maxwellian moleculescan be represented through the product of two elementary stochastic processes. The first one is the Brownian motion on the group of rotations. The second one is, conditionally on the first one, a Gaussian process. Using this representation, we establish sharp multi-scale upper and lower bounds for the transition density of the Landau equation, the multi-scale structure depending on the shape of the support of the initial condition.en
• dc.description.sponsorship For the second author, the article was prepared within the framework of a subsidy granted to the HSE by the Government of the Russian Federation for the implementation of the Global Competitiveness Program. Third author acknowledges support from the European Union programme FP7-PEOPLE-2012-CIG under grant agreement 333938.
• dc.format.mimetype application/pdf
• dc.identifier.citation Delarue F, Menozzi S, Nualart E. The Landau equation for Maxwellian molecules and the Brownian motion on SON(R). Electron J Probab. 2015;20(92):[39 p.]. DOI: 10.1214/EJP.v20-4012
• dc.identifier.doi http://dx.doi.org/10.1214/EJP.v20-4012
• dc.identifier.issn 1083-6489
• dc.identifier.uri http://hdl.handle.net/10230/34386
• dc.language.iso eng
• dc.publisher Institute of Mathematical Statistics (IMS)ca
• dc.relation.ispartof Electronic Journal of Probability. 2015;20(92):[39 p.]
• dc.relation.projectID info:eu-repo/grantAgreement/EC/FP7/333938
• dc.rights This article is published with a Creative Commons Attribution Licence (CC BY 2.5)
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.rights.uri http://creativecommons.org/licenses/by/2.5/legalcode
• dc.subject.keyword Landau equation for Maxwellian moleculesen
• dc.subject.keyword Stochastic analysisen
• dc.subject.keyword Heat kernel estimates on groupsen
• dc.subject.keyword Large deviationsen
• dc.title The Landau equation for Maxwellian molecules and the Brownian motion on SON(R)ca
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/publishedVersion