论文标题
近似于Erdös-rényi随机图中三角形的累积生成函数
Approximating the cumulant generating function of triangles in the Erdös-Rényi random graph
论文作者
论文摘要
我们研究了“边缘三角模型”的压力，该模型等同于Erdös-rényi随机图中三角形的累积生成函数。通过分析增加体积的有限图以及无限体积限制中的图形变异问题，我们将曲线定位在参数空间中，其中发生一个单步复制对称性破坏过渡。在破碎的对称相中对大图进行采样的图形很好地描述了一个结构，其结构非常接近Equi-tigi-timite图。
We study the pressure of the "edge-triangle model", which is equivalent to the cumulant generating function of triangles in the Erdös-Rényi random graph. By analyzing finite graphs of increasing volume, as well as the graphon variational problem in the infinite volume limit, we locate a curve in the parameter space where a one-step replica symmetry breaking transition occurs. Sampling a large graph in the broken symmetry phase is well described by a graphon with a structure very close to the one of an equi-bipartite graph.
