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2015 The Landau equation for Maxwellian molecules and the Brownian motion on $SO_N(\mathbb{R})$
François Delarue, Stéphane Menozzi, Eulalia Nualart
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Electron. J. Probab. 20: 1-39 (2015). DOI: 10.1214/EJP.v20-4012

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.

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François Delarue. Stéphane Menozzi. Eulalia Nualart. "The Landau equation for Maxwellian molecules and the Brownian motion on $SO_N(\mathbb{R})$." Electron. J. Probab. 20 1 - 39, 2015. https://doi.org/10.1214/EJP.v20-4012

Information

Accepted: 10 September 2015; Published: 2015
First available in Project Euclid: 4 June 2016

zbMATH: 1328.60159
MathSciNet: MR3399828
Digital Object Identifier: 10.1214/EJP.v20-4012

Subjects:
Primary: 60H30
Secondary: 60H10, 60H40

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