Renormalization-group perspective on spontaneous stochasticity

TL;DR

This paper applies a renormalization-group framework to understand spontaneous stochasticity in turbulence, revealing it as a universal fixed point phenomenon analogous to other universality classes in physics.

Contribution

It introduces a novel RG perspective on spontaneous stochasticity, connecting turbulence to universal fixed points and classical models within a unified multiscale dynamical systems approach.

Findings

Spontaneous stochasticity emerges as a universal RG fixed point.

The framework unifies turbulence phenomena with classical models like Feigenbaum and CLT.

Spontaneous stochasticity is shown to be independent of microscopic regularization.

Abstract

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.