论文标题
在边缘三角形模型中存在对称双相阶段
Existence of a symmetric bipodal phase in the edge-triangle model
论文作者
论文摘要
在边缘密度接近1/2的边缘三角形模型中，三角形密度以下1/8，我们证明了唯一的熵最大化的图形是对称的两倍。我们还证明，对于任何边缘密度$ e $少于$ e_0 =（3- \ sqrt {3}）/6 \大约0.2113 $，三角形密度略低于$ e^3 $，entrogy-Mammamamimimizing graphon不是对称的两倍。
In the edge-triangle model with edge density close to 1/2 and triangle density below 1/8 we prove that the unique entropy-maximizing graphon is symmetric bipodal. We also prove that,for any edge density $e$ less than $e_0 = (3-\sqrt{3})/6 \approx 0.2113$ and triangle density slightly less than $e^3$, the entropy-maximizing graphon is not symmetric bipodal.
