Renormalization-group perspective on spontaneous stochasticity
Chaotic Dynamics
2026-03-02 v1
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.
Cite
@article{arxiv.2602.24221,
title = {Renormalization-group perspective on spontaneous stochasticity},
author = {Alexei A. Mailybaev and Luca Moriconi},
journal= {arXiv preprint arXiv:2602.24221},
year = {2026}
}
Comments
28 pages, 10 figures