Abstract
We consider a metric for probability densities with finite variance on ℝd, and compare it with other metrics. We use it for several applications both in probability and in kinetic theory. The main application in kinetic theory is a uniqueness result for the solution of the spatially homogeneous Boltzmann equation for a gas of true Maxwell molecules.
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Toscani, G., Villani, C. Probability Metrics and Uniqueness of the Solution to the Boltzmann Equation for a Maxwell Gas. Journal of Statistical Physics 94, 619–637 (1999). https://doi.org/10.1023/A:1004508706950
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DOI: https://doi.org/10.1023/A:1004508706950