Pivot probabilities and norm effects in Gaussian elimination for $\beta$-ensembles

Kenji Gunawan; John Peca-Medlin

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arXiv · 2506.20470

Pivot probabilities and norm effects in Gaussian elimination for $\beta$-ensembles

Kenji Gunawan·John Peca-Medlin

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Abstract

We analyze pivot probabilities in Gaussian elimination with partial pivoting (GEPP) for $2 \times 2$ random matrix ensembles. For GUE matrices, we resolve a previously reported discrepancy between theoretical predictions and empirical observations by deriving the exact pivot probability under standard LAPACK-style implementations. We further show that Dumitriu-Edelman tridiagonal $\beta$-ensembles agree with the earlier theoretical expectations.

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Kenji Gunawan, John Peca-Medlin. 2025-06-25. Pivot probabilities and norm effects in Gaussian elimination for $\beta$-ensembles. https://arxiv.org/abs/2506.20470

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