Constructs scaling limit of SU(2) lattice Yang-Mills-Higgs theory in d≥2 showing stereographic projection of gauge field converges to massive Gaussian under specific scaling αg = cε and g = O(ε^{50d}), first rigorous mass generation by Higgs mechanism for non-Abelian case.
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Global existence holds for 2D generalized PAM on R^2 for every noise roughness 0<κ<√5−2, with uniqueness when F'' is globally Lipschitz.
Proves that SO(3) lattice Yang-Mills theory fails Wilson's confinement criterion at strong coupling.
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A scaling limit of $\mathrm{SU}(2)$ lattice Yang-Mills-Higgs theory
Constructs scaling limit of SU(2) lattice Yang-Mills-Higgs theory in d≥2 showing stereographic projection of gauge field converges to massive Gaussian under specific scaling αg = cε and g = O(ε^{50d}), first rigorous mass generation by Higgs mechanism for non-Abelian case.
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Global well-posedness for generalized parabolic Anderson model on the whole plane
Global existence holds for 2D generalized PAM on R^2 for every noise roughness 0<κ<√5−2, with uniqueness when F'' is globally Lipschitz.
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Deconfinement For $\mathrm{SO}(3)$ Lattice Yang-Mills at Strong Coupling
Proves that SO(3) lattice Yang-Mills theory fails Wilson's confinement criterion at strong coupling.