临界Liouville量子球面与q=4时FK映射的几何极限
The critical Liouville quantum sphere and geometric limits of FK maps at q=4
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具体内容
稿件研究单位面积临界Liouville量子球面，作者声称将其构造为普通次临界量子球面的极限，并赋予临界内蕴度量。摘要表示证明了q=4的球面Fortuin–Kasteleyn平面图在等边旗标均匀化嵌入下联合收敛到该球面，并装饰以独立嵌套共形圈系综CLE4；在确定性距离归一化下，收敛包括面积测度、完整嵌入距离函数及所有正整数边数下的宏观界面。该结果把随机平面图的标度极限与Liouville量子引力联系起来。
- 构造单位面积临界Liouville量子球面为次临界量子球面极限并赋予临界内蕴度量。
- q=4球面FK平面图经等边旗标均匀化联合收敛到该球面并装饰CLE4。
- 确定性距离归一化下收敛含面积测度、嵌入距离函数与各边数宏观界面。
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英文原始摘要
We construct the field and area law of the unit-area critical Liouville quantum sphere as a limit of ordinary subcritical quantum spheres, and equip it with its critical intrinsic metric. We then prove that spherical Fortuin–Kasteleyn planar maps at q = 4, embedded by their equilateral flag uniformizations, converge jointly to this sphere decorated by an independent nested conformal loop ensemble CLE4. With deterministic distance normalization, the convergence includes the area measure, the full embedded distance function, and every macroscopic interface through all positive integer edge counts.
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