## Electronic Journal of Probability

### The Landau equation for Maxwellian molecules and the Brownian motion on $SO_N(\mathbb{R})$

#### 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.

#### Article information

Source
Electron. J. Probab., Volume 20 (2015), paper no. 92, 39 pp.

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

https://projecteuclid.org/euclid.ejp/1465067198

Digital Object Identifier
doi:10.1214/EJP.v20-4012

Mathematical Reviews number (MathSciNet)
MR3399828

Zentralblatt MATH identifier
1328.60159

Rights

#### Citation

Delarue, François; Menozzi, Stéphane; Nualart, Eulalia. The Landau equation for Maxwellian molecules and the Brownian motion on $SO_N(\mathbb{R})$. Electron. J. Probab. 20 (2015), paper no. 92, 39 pp. doi:10.1214/EJP.v20-4012. https://projecteuclid.org/euclid.ejp/1465067198

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