A Productization Property/Trick For H-Stable(And Hopefully Strongly Log-Concave) Polynomials
summary
Claims a productization trick that locally expresses many H-stable (real-stable) polynomials as a product of simpler “product polynomials” built from matrices whose row and column sums meet prescribed vectors, uses matrix eigen/Schur decompositions and semi‑algebraic reductions, and converts known matrix capacity/permanent bounds into polynomial coefficient lower bounds. Provides a polynomial-time zero test for the infimum over that polytope, shows L1 condition (not L2) is the natural necessary/sufficient closeness measure, and drives improved van der Waerden–style bounds used in recent traveling‑salesman work.
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