Gamma-convergence of fractional Gaussian perimeter

2021/03/30 by Alessandro Carbotti, Carbotti, Alessandro, Simone Cito +5
Mathematics · #35R11 #49Q20 #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2103.16598

openalex publication_date 2021/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the Γ-convergence of the renormalised fractional Gaussian 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.

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