On the Widom–Rowlinson Occupancy Fraction in Regular Graphs
On the Widom–Rowlinson Occupancy Fraction in Regular Graphs
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关于正则图中的 Widom-Rowlinson 占有率
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
P. Tetali
中科院分区：
文献类型：
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作者：
E. Cohen;Will Perkins;P. Tetali
我们考虑了D-Rectarty粒子上的两种相互作用的粒子的宽度 - Rowlinson模型通过在D+1顶点上的完整图，K D+1作为推论来实现。 d-regular图表明，从任何D-graph g到图形HWR的同态数字的特殊情况，在每个顶点上有一个环上的路径Galvin的概念。
We consider the Widom–Rowlinson model of two types of interacting particles on d-regular graphs. We prove a tight upper bound on the occupancy fraction, the expected fraction of vertices occupied by a particle under a random configuration from the model. The upper bound is achieved uniquely by unions of complete graphs on d + 1 vertices, K d+1. As a corollary we find that K d+1 also maximizes the normalized partition function of the Widom–Rowlinson model over the class of d-regular graphs. A special case of this shows that the normalized number of homomorphisms from any d-regular graph G to the graph HWR , a path on three vertices with a loop on each vertex, is maximized by K d+1. This proves a conjecture of Galvin.