A Probabilistic Mechanism for Quark Confinement
summary
Claims that strong mass gap (exponential decay of truncated correlations under arbitrary boundary conditions) together with a nontrivial center symmetry implies Wilson's area law for rectangular loops in lattice gauge theory. Proof is fully probabilistic: partition space into time slabs, condition on slab boundaries, build repeated cube couplings to show exponential coupling success toward the slab center, deduce area decay and a unique infinite-volume Gibbs state. Result holds for compact connected matrix groups with a center and any dimension, given the decay assumption.
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