AI 中文总结
该研究针对临界二维随机热流与二维定向聚合物模型，通过改进测度变换论证并引入新颖粗粒化程序，给出了在所有参数下均一致的分数阶矩估计，明确其消失由二阶矩发散主导，还提供了定向聚合物的精确二阶矩估计。
AI 中文摘要
我们估计了临界二维随机热流分配给小球的归一化质量的分数阶矩，所得结果也涵盖对应二维定向聚合物模型的离散情形，且提供了在所有参数下均一致的估计。本研究的关键结论是：分数阶矩的消失完全由二阶矩的发散所主导。我们采用一种相当稳健的方法，通过改进测度变换论证并引入一种新颖的粗粒化程序，将证明过程简化为本质上的二阶矩估计（事实上，我们还为定向聚合物提供了具有独立研究价值的精确二阶矩估计）。
英文摘要
We estimate the fractional moments of the normalized mass assigned by the Critical 2D Stochastic Heat Flow to small balls. Our results also cover the discrete case corresponding to the 2D directed polymer model and provide estimates that are uniform in all parameters. One key takeaway of our results is that the vanishing of the fractional moments is completely governed by the divergence of the second moment. We use a quite robust method, by refining the change of measure argument and introducing a novel coarse-graining procedure, reducing the proof to essentially second moment estimates (in fact, we also provide sharp second moment estimates for directed polymers, of independent interest).
Comments26 pages, 1 figure
