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<p>In this paper, we study fluctuations and moderate deviations for a discrete energy Kac-like walk associated with a Boltzmann-type equation. We show that the fluctuations of the empirical measure around the Boltzmann-type equation converge in law to an infinite dimensional Ornstein-Uhlenbeck process, and establish the moderate deviation principle for the empirical measure.</p>

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Fluctuations and Moderate Deviations for a Binary Collision Model

  • 期刊论文

  • 发表日期：

    2026年1月29日

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  • Fuqing Gao,
  • Xianjie Xia

摘要

In this paper, we study fluctuations and moderate deviations for a discrete energy Kac-like walk associated with a Boltzmann-type equation. We show that the fluctuations of the empirical measure around the Boltzmann-type equation converge in law to an infinite dimensional Ornstein-Uhlenbeck process, and establish the moderate deviation principle for the empirical measure.