费米统计和其他条件积测度的抽样
Sampling the Fermi statistics and other conditional product measures
摘要：
通过一个单步计算量为一阶的Metropolis类算法，我们建立了一个马尔可夫链，它对m个能级中的k个非相互作用粒子松弛到正则费米统计.均匀的温度以及能量值和能级的简并度，我们给出了一个明确的上界与首项公里（lnk）的混合时间的动力学。我们得到这样的建设和上界作为一个特殊情况下的一般结果（非齐次）产品的超对数凹措施（如二项式或泊松定律）的整体约束。作为这个一般结果的结果，我们也得到了一个无序无关的上界上的一个简单的排它过程的混合时间的完全图与网站无序。这个一般结果是基于一个基本的耦合参数，并扩展到（非齐次）产品的对数凹措施。
英文摘要：
Through a Metropolis-like algorithm with single step computational cost of order one, we build a Markov chain that relaxes to the canonical Fermi statistics for k non-interacting particles among m energy levels. Uniformly over the temperature as well as the energy values and degeneracies of the energy levels we give an explicit upper bound with leading term km(ln k) for the mixing time of the dynamics. We obtain such construction and upper bound as a special case of a general result on (non-homogeneous) products of ultra log-concave measures (like binomial or Poisson laws) with a global constraint. As a consequence of this general result we also obtain a disorder-independent upper bound on the mixing time of a simple exclusion process on the complete graph with site disorder. This general result is based on an elementary coupling argument and extended to (non-homogeneous) products of log-concave measures.
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