On the Kolmogorov-Feller weak law of large numbers for the Fréchet mean on non-compact symmetric spaces

Jongmin Lee; Sungkyu Jung

doi:10.1016/j.spl.2026.110875

paper

On the Kolmogorov-Feller weak law of large numbers for the Fréchet mean on non-compact symmetric spaces

arXiv:2509.02074 · doi:10.1016/j.spl.2026.110875

Abstract

We prove the Kolmogorov-Feller weak law of large numbers for sample Fréchet means on non-compact symmetric spaces. The result covers independent, non-identically distributed data, extending beyond the i.i.d. setting. Examples of symmetric positive-definite matrices and product symmetric spaces are provided.