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

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dc.contributor.author	Delarue, François
dc.contributor.author	Menozzi, Stéphane
dc.contributor.author	Nualart, Eulàlia
dc.date	2015
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.citation	1083-6489
dc.identifier.citation	http://dx.doi.org/10.1214/EJP.v20-4012
dc.identifier.uri	http://hdl.handle.net/10230/34386
dc.format	application/pdf
dc.language.iso	eng
dc.publisher	Institute of Mathematical Statistics (IMS)
dc.relation	Electronic Journal of Probability. 2015;20(92): 39 p.
dc.relation	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	info:eu-repo/semantics/openAccess
dc.rights	http://creativecommons.org/licenses/by/2.5/legalcode
dc.subject	Landau equation for Maxwellian molecules
dc.subject	Stochastic analysis
dc.subject	Heat kernel estimates on groups
dc.subject	Large deviations
dc.title	The Landau equation for Maxwellian molecules and the Brownian motion on SON(R)
dc.type	info:eu-repo/semantics/article
dc.type	info:eu-repo/semantics/publishedVersion
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.
dc.description.abstract	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.

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