The finite R-transform of a polynomial differs from the Voiculescu R-transform of its empirical root distribution by O(N^{-1}), providing an analytic proof that finite free additive convolution converges to free additive convolution.
Finite free information inequalities
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Computational discovery via FlowBoost supports conjectures on the singular values of the coupling matrix E_n being 2^{-k/2} independent of n, a sharp p=2 critical exponent for p-Stam inequalities, and bifurcation of extremals for p<2.
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An analytic approach to the finite R-transform
The finite R-transform of a polynomial differs from the Voiculescu R-transform of its empirical root distribution by O(N^{-1}), providing an analytic proof that finite free additive convolution converges to free additive convolution.
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Spectral Structure in Finite Free Information Inequalities and $p$-Stam Phase Transitions
Computational discovery via FlowBoost supports conjectures on the singular values of the coupling matrix E_n being 2^{-k/2} independent of n, a sharp p=2 critical exponent for p-Stam inequalities, and bifurcation of extremals for p<2.