Volume-Independent Spectral Gap for Strong-Coupling Lattice Gauge Theory via Poincare-Dobrushin Machinery

We prove a volume-independent spectral gap for SU(N) lattice gauge theory in the strong-coupling regime (β < 1/36) using Holley–Stroock and Dobrushin–Zegarlinski tensorisation. A restricted Poincaré inequality on typical sets achieves exp(-O(√β)) scaling, improving over the naive exp(-O(β)). We introduce defective Dobrushin conditions with annealed influence coefficients, an RG-Gronwall lemma for polynomially degrading LSI constants, and a Γ-convergence formulation of the block-spin RG flow via Kingman's subadditive ergodic theorem. The continuum mass gap is conditional on correlation-length contraction under block-spin RG. Published in English and German versions. Part of the Functional Stability Theory (FST) programme.