发表机构
CNRS & Laboratoire Jacques-Louis Lions, Sorbonne Université; Courant Institute of Mathematical Sciences, New York University; Department of Mathematics, University of Pennsylvania; Department of Mathematics and Statistics, University of Helsinki（法国国家科学研究中心与雅克-路易·利翁斯实验室，索邦大学; 纽约大学库朗数学科学研究所; 宾夕法尼亚大学数学系; 赫尔辛基大学数学与统计系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究d≥2维对数相关高斯势中漂移的布朗粒子，证明弱无序下其收敛到与布朗运动奇异的标度极限，不变测度为高斯乘性混沌，通过重整化群归纳法证明并精确计算二维下的扩散系数衰减指数。
AI 中文摘要
我们研究d≥2维欧氏空间ℝ^d中，漂移项由对数相关高斯势梯度给出的布朗粒子。在弱无序条件下，我们证明其收敛到一个标度极限，该极限的律相对于布朗运动是奇异的，且其不变测度由高斯乘性混沌给出。证明采用重整化群归纳法：在每个尺度上，椭圆算子可由有效扩散系数随尺度幂次衰减的拉普拉斯算子很好近似。我们在二维情形精确计算了该指数。
英文摘要
We study a Brownian particle in $\mathbb{R}^d$, $d\geq2$, with drift given by the gradient of a log-correlated Gaussian potential. At weak disorder, we prove convergence to a scaling limit whose law is singular with respect to Brownian motion and whose invariant measure is given by Gaussian multiplicative chaos. The proof uses a renormalization group induction: at each scale, the elliptic operator is well approximated by a Laplacian with effective diffusivity decaying as a power of scale. We compute this exponent exactly in dimension two.
Comments206 pages, 1 figure, Lean formalization at https://github.com/nitromannitol/subdiffusive-process
