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

Jongmin Lee; Sungkyu Jung

doi:10.1016/j.spl.2026.110875

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arXiv · 2509.02074

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

Jongmin Lee·Sungkyu Jung

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Abstract

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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Jongmin Lee, Sungkyu Jung. 2025-09-02. On the Kolmogorov-Feller weak law of large numbers for the Fr\'echet mean on non-compact symmetric spaces. https://doi.org/10.1016/j.spl.2026.110875

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