Spontaneous Stochasticity and Renormalization Group in Discrete Multi-scale Dynamics

We introduce a class of multi-scale systems with discrete time, motivated by the problem inviscid limit in fluid dynamics presence small-scale noise. These are infinite-dimensional and defined on scale-invariant space-time lattice. propose qualitative theory describing vanishing regularization (inviscid) as an attractor renormalization group operator acting space flow maps or respective probability kernels. If is nontrivial kernel, we say that spontaneously stochastic: it defines stochastic (Markov) process solving deterministic equations initial boundary conditions. The results illustrated solvable models: symbolic leading to digital turbulence expanding interacting phases.