Weak universality of dynamical $Φ^4_3$: non-Gaussian noise
Weak universality of dynamical $Φ^4_3$: non-Gaussian noise
We consider a class of continuous phase coexistence models in three spatial dimensions. The fluctuations are driven by symmetric stationary random fields with sufficient integrability and mixing conditions, but not necessarily Gaussian. We show that, in the weakly nonlinear regime, if the external potential is a symmetric polynomial and a certain average of it exhibits pitchfork bifurcation, then these models all rescale to $Φ^4_3$ near their critical point.
37 pages; updated introduction and references
- University of Warwick United Kingdom
- King’s University United States
- University of Oxford United Kingdom
- Columbia University United States
- Columbia University United States
non-Gaussian fluctuation, polynomial potential, Probability (math.PR), FOS: Physical sciences, phase coexistence, Mathematical Physics (math-ph), Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems, Stochastic partial differential equations (aspects of stochastic analysis), Infinite-dimensional random dynamical systems; stochastic equations, FOS: Mathematics, PDEs with randomness, stochastic partial differential equations, Mathematical Physics, Mathematics - Probability, Singular perturbations in context of PDEs
non-Gaussian fluctuation, polynomial potential, Probability (math.PR), FOS: Physical sciences, phase coexistence, Mathematical Physics (math-ph), Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems, Stochastic partial differential equations (aspects of stochastic analysis), Infinite-dimensional random dynamical systems; stochastic equations, FOS: Mathematics, PDEs with randomness, stochastic partial differential equations, Mathematical Physics, Mathematics - Probability, Singular perturbations in context of PDEs
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