论文标题
能量增加溶液的渐近概率
Asymptotic probability of energy increasing solutions to the homogeneous Boltzmann equation
论文作者
论文摘要
Lu和Wennberg构建了均匀的玻尔兹曼方程的弱解决方案。我们考虑了具有二进制碰撞（KAC模型）的潜在微观随机模型，并表明这些解决方案是非典型的。更确切地说，我们证明观察这些路径的概率在颗粒数量中呈指数级，并计算指数率。通过改善规范环境中既定的大偏差估计值来获得该结果。关键成分是在微域中的KAC模型中扩展了Sanov定理到微型典型的集合和大偏差。
Weak solutions to the homogeneous Boltzmann equation with increasing energy have been constructed by Lu and Wennberg. We consider an underlying microscopic stochastic model with binary collision (Kac's model) and show that these solutions are atypical. More precisely, we prove that the probability of observing these paths is exponentially small in the number of particles and compute the exponential rate. This result is obtained by improving the established large deviation estimates in the canonical setting. Key ingredients are the extension of Sanov's theorem to the microcanonical ensemble and large deviations for the Kac's model in the microcanonical setting.
