On the Kolmogorov-Feller weak law of large numbers for the Fr\'echet mean on non-compact symmetric spaces

Jongmin Lee; Sungkyu Jung

arxiv: 2509.02074 · v2 · pith:WQOWOKSInew · submitted 2025-09-02 · 🧮 math.PR · math.ST· stat.TH

On the Kolmogorov-Feller weak law of large numbers for the Fr\'echet mean on non-compact symmetric spaces

Jongmin Lee , Sungkyu Jung This is my paper

classification 🧮 math.PR math.STstat.TH

keywords symmetricspacesechetkolmogorov-fellerlargenon-compactnumbersweak

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We prove the Kolmogorov-Feller weak law of large numbers for sample Fr\'echet 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.

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