The Multifractal Nature of Boltzmann Processes

2015/04/25 by Liping Xu, Xu, Liping · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Probability (math.PR) #Statistical Mechanics and Entropy #Theoretical and Computational Physics #math.PR

paper · pdf · doi:10.48550/arxiv.1504.06725

arxiv created 2015/04/25 · openalex publication_date 2015/04/25 · arxiv updated 2015/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the spatially homogeneous Boltzmann equation for (true) hard and moderately soft potentials. We study the pathwise properties of the stochastic process (V_t)_{t≥ 0}, which describes the time evolution of the velocity of a typical particle. We show that this process is almost surely multifractal and we compute its spectrum of singularities. For hard potentials, we also compute the multifractal spectrum of the position process (X_t)_t≥0.

Citations

• Fractal Geometry: Mathematical Foundations and Applications.

Cited by

• Uniqueness and propagation of chaos for the Boltzmann equation with moderately soft potentials

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