标题： 共形环的共形半径 显示英文标题

标题： Conformal radii for conformal loop ensembles

摘要： 共形循环系集 CLE(k)，定义于 k ∈ [8/3, 8]，是在平面区域中的随机环集合，据推测是 O(n) 环模型的缩放极限。 我们计算了围绕确定点的嵌套环的共形半径分布。 我们的结果与 Cardy 和 Ziff 以及 Kenyon 和 Wilson 对 O(n) 模型的预测一致。 我们还计算了 CLE(k) 的格子结构的期望维度，该结构由未被任何环包围的点组成，结果为 2-(8-k)(3k-8)/32k，这与 Duplantier 给出的 O(n) 模型格子结构的分形维度一致。 显示英文摘要

摘要： The conformal loop ensembles CLE(k), defined for k in [8/3, 8], are random collections of loops in a planar domain which are conjectured scaling limits of the O(n) loop models. We calculate the distribution of the conformal radii of the nested loops surrounding a deterministic point. Our results agree with predictions made by Cardy and Ziff and by Kenyon and Wilson for the O(n) model. We also compute the expectation dimension of the CLE(k) gasket, which consists of points not surrounded by any loop, to be 2-(8-k)(3k-8)/32k, which agrees with the fractal dimension given by Duplantier for the O(n) model gasket.