Gamma-convergence of Gaussian fractional perimeter

Abstract

We prove the Γ-convergence of the renormalised Gaussian fractional s-perimeter to the Gaussian perimeter as s→1−. Our definition of fractional perimeter comes from that of the fractional powers of Ornstein–Uhlenbeck operator given via Bochner subordination formula. As a typical feature of the Gaussian setting, the constant appearing in front of the Γ-limit does not depend on the dimension.