Kac主方程谱隙的确定及其随机演化
Determination of the Spectral Gap for Kac's Master Equation and Related Stochastic Evolutions
摘要：
我们提出了一种方法的绑定，并在某些情况下计算，频谱间隙的系统的许多粒子的随机碰撞机制的影响下发展。特别是，该方法产生精确的光谱间隙的模型，由于马克卡茨的能量守恒碰撞一维速度。它也是足够强大的，以提供定性的尖锐的界限，也在物理上更现实的动量和能量守恒碰撞的情况下，在三维，以及一系列相关的模型。
英文摘要：
We present a method for bounding, and in some cases computing, the spectral gap for systems of many particles evolving under the influence of a random collision mechanism. In particular, the method yields the exact spectral gap in a model due to Mark Kac of energy conserving collisions with one dimensional velocities. It is also sufficiently robust to provide qualitatively sharp bounds also in the case of more physically realistic momentum and energy conserving collisions in three dimensions, as well as a range of related models.
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