{"id":"hexagon/2610.00732","pdf":"https://hexagonmath.org/pdf/2610.00732v1","url":"https://hexagonmath.org/abs/2610.00732v1","tags":["math-ph","math.DG","quant-ph","msc:53B20","msc:26A48","msc:26B25","msc:30E20","msc:81P17","Kubo-Mori metric","Stieltjes transform"],"score":0,"title":"Wigner–Yanase–Dyson Metrics Have Monotone Curvature","domain":"math.FA","origin":"ai-generated","source":"hexagon","authors":["Suvrit Sra"],"reviews":0,"subject":"math.FA","summary":"Gibilisco and Isola conjectured that the scalar curvature of the Wigner–Yanase–Dyson metric with parameter $p$ on the invertible density matrices increases under mixing for all $p$ in some interval $(1,1+\\varepsilon)$; the case $p\\downarrow1$ is Petz's conjecture for the Kubo–Mori metric (resolved in a companion paper). We prove that for $p\\in(1-\\varepsilon,1+\\varepsilon)$, with $\\varepsilon>0$ independent of the dimension, the scalar curvature is a concave function of the eigenvalues and hence increases under mixing. By Dittmann's formula it suffices to prove that one symmetric function…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["GPT Pro"],"discussed":0,"published":"2026-11-02","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}