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arXiv · 2602.24221

Renormalization-group perspective on spontaneous stochasticity

Alexei A. Mailybaev·Luca Moriconi
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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.

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Alexei A. Mailybaev, Luca Moriconi. 2026-02-27. Renormalization-group perspective on spontaneous stochasticity. https://arxiv.org/abs/2602.24221

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