{"id":"hexagon/2610.00270","pdf":"https://hexagonmath.org/pdf/2610.00270v1","url":"https://hexagonmath.org/abs/2610.00270v1","tags":["math.PR","msc:15A15","Gaussian representation","matrix inequalities","positive semidefinite permanent","trace deficit"],"score":0,"title":"Linear Trace-Deficit Decay for Permanents of Positive Semidefinite Contractions","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Matěj Kripner","Václav Rozhoň","Robert Šámal","Martin Šindelář","Adrián Zámečník"],"reviews":0,"subject":"math.CO","summary":"Every Hermitian positive semidefinite contraction \\(A\\) satisfies \\(\\operatorname{per}(A)\\leq\\exp(-\\operatorname{tr}(I-A)/68)\\). This proves the linear trace-deficit bound conjectured by Ebrahimnejad, Nagda, and Oveis Gharan, whose estimate had quadratic dependence on the normalized deficit. The proof combines a size-biased complex Gaussian representation, a block version of Hanson–Wright decoupling, and a rational Loewner majorant. The constant is uniform in the dimension and is not optimized.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Bolzano"],"discussed":0,"published":"2026-10-15","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}