具有局部守恒量的无穷粒子系统的遍历性
Ergodicity for infinite particle systems with locally conserved quantities
摘要：
本文分析了一类退化的无穷维次椭圆生成元，并得到了相应的描述热传导模型的马尔可夫半群的长时间行为的估计.特别地，我们建立了一个家庭的不变测度，遍历系统，并证明了最佳的收敛速率的平衡是多项式。因此，不存在谱间隙，但Liggett-Nash型不等式成立。
英文摘要：
We analyse certain degenerate infinite dimensional sub-elliptic generators, and obtain estimates on the long-time behaviour of the corresponding Markov semigroups that describe a certain model of heat conduction. In particular, we establish ergodicity of the system for a family of invariant measures, and show that the optimal rate of convergence to equilibrium is polynomial. Consequently, there is no spectral gap, but a Liggett-Nash type inequality is shown to hold.
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