对自发随机性的重整化群视角
Renormalization-group perspective on spontaneous stochasticity
AI总结：
本文从重整化群视角探讨流体湍流中自发随机性，通过多尺度动力系统框架揭示其作为普遍固定点的本质，并重新诠释经典例子。
摘要：
我们从多尺度动力系统的角度，提出了对流体湍流中自发随机性的重整化群视角。基于之前已建立的可解多尺度阿诺德猫模型结果，我们展示自发随机性作为重整化群变换作用于马尔可夫核的普遍固定点，与微观正则化无关。经典例子——包括费根鲍姆方程、中心极限定理和分层自旋模型——都在同一框架下重新解释，将自发随机性置于其他普遍现象之中。
英文摘要：
We present a renormalization-group perspective on spontaneous stochasticity in hydrodynamic turbulence, viewed through the lens of multiscale dynamical systems. Building on previously established results for a solvable multiscale Arnold's cat model, we show that spontaneous stochasticity emerges as a universal fixed point of an RG transformation acting on Markov kernels, independent of the microscopic regularization. Classical examples - including the Feigenbaum equation, the central limit theorem, and hierarchical spin models - are reinterpreted within the same framework, placing spontaneous stochasticity alongside other universality phenomena.
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