FlowBoost finds the Hermite pair as the unique equality case for the p=2 finite free Stam inequality, conjectures that the singular values of the coupling matrix E_n are 2^{-k/2} independent of n, and reveals a phase transition at the critical exponent p*=2 with bifurcating extremals for p<2.
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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.
t-deformed convolution and cumulants on formal power series yield LLN and CLT analogues that recover classical convolution at t=-1 and finite free generators at t=d, with explicit infinitesimal generators for the associated semigroups.
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FlowBoost Reveals Phase Transitions and Spectral Structure in Finite Free Information Inequalities
FlowBoost finds the Hermite pair as the unique equality case for the p=2 finite free Stam inequality, conjectures that the singular values of the coupling matrix E_n are 2^{-k/2} independent of n, and reveals a phase transition at the critical exponent p*=2 with bifurcating 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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Convolution, cumulants and infinitesimal generators in the formal power series ring
t-deformed convolution and cumulants on formal power series yield LLN and CLT analogues that recover classical convolution at t=-1 and finite free generators at t=d, with explicit infinitesimal generators for the associated semigroups.