具有并行更新和异质逸度的Glauber动力学的混合时间
Mixing Time of Glauber Dynamics With Parallel Updates and Heterogeneous Fugacities
摘要：
Glauber动力学是一个强有力的工具来产生随机的，近似解组合困难的问题。应用包括马尔可夫链蒙特卡罗（MCMC）模拟和无线网络的分布式调度。在本文中，我们推导出混合时间的一个广义的Glauber动力学的多个顶点被允许并行更新他们的状态和逸度的每个顶点可以是不同的界限。这些结果可以用来得到系统参数如逸度、顶点度和更新概率的各种条件，在这些条件下，混合时间以顶点数的多项式形式增长。
英文摘要：
Glauber dynamics is a powerful tool to generate randomized, approximate solutions to combinatorially difficult problems. Applications include Markov Chain Monte Carlo (MCMC) simulation and distributed scheduling for wireless networks. In this paper, we derive bounds on the mixing time of a generalization of Glauber dynamics where multiple vertices are allowed to update their states in parallel and the fugacity of each vertex can be different. The results can be used to obtain various conditions on the system parameters such as fugacities, vertex degrees and update probabilities, under which the mixing time grows polynomially in the number of vertices.
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