Spontaneous stochasticity in discrete dynamics on a scale-invariant lattice
Artem Raibekas (UFF)


The notion of spontaneous stochasticity comes from models in fluid dynamics involving partial differential equations with space-time scale invariance. A feature of these equations is that the solutions may be not-unique or not globally defined. In this case, a globally well-posed system may be obtained by adding ”regularizing” terms and a physically relevant solution is selected in the limit of the vanishing regularization. Moreover, with the addition of noise to the regularization, in the limit one may obtain the so-called spontaneous stochastic solutions. In this work we propose discrete dynamical models on a scale-invariant space-time lattice which are solvable and theoretically describe the phenomenon of spontaneous stochasticity. This is a joint work with Alexei Mailybaev (IMPA).


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