Infrared Stabilization and Stochastic Spectral Gap Formation in Lattice Yang–Mills Theory

This work introduces a framework for infrared stabilization in lattice Yang–Mills theory based on an active spectral projection mechanism acting on low-lying modes of the Faddeev–Popov operator. We establish a functional-analytic setting in which the modified dynamics exhibit infrared exponential integrability, tightness of projected components, and quasi-local behavior under Combes–Thomas bounds. Under suitable assumptions, a Bakry–Émery-type coercivity condition yields a strictly positive spectral gap for the associated stochastic generator. Numerical simulations on SU(3) lattice ensembles provide evidence for the persistence of this gap in the thermodynamic limit and demonstrate a substantial reduction in autocorrelation times. The results isolate structural mechanisms for infrared stabilization and stochastic gap formation. A full constructive treatment of Yang–Mills theory, including reflection positivity and continuum reconstruction, remains an open problem.