发表机构
TIFR Mumbai（塔塔基础研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
从两个独立对角变形的 GUE 矩阵各自的变量经子式过程形成双蜂巢并应用八面体递推，在匹配条件下，证明所得蜂巢律在相对熵上接近 GUE 蜂巢律。
AI 中文摘要
我们从变形的 GUE 子式过程构造随机蜂巢。从两个独立对角变形的 GUE 矩阵出发，利用它们的子式过程形成双蜂巢并应用八面体递推。在匹配条件下，证明所得蜂巢律在相对熵上接近 GUE 蜂巢律，给出了相关公式及参数关系，实现了在直角和钝角区域直至次主导相对熵的 GUE 蜂巢律。附录记录了两个明确的表面张力近似和数值比较，它们推动了构造。
英文摘要
We construct random hives from deformed GUE minor processes. Starting from two independent diagonally deformed GUE matrices \[ X=\sqrt{n}(wG+uD),\qquad Y=\sqrt{n}(w'G'+u'D'), \] where \(D,D'\) are diagonal and have GUE spectra, we use their minor processes to form a double hive and then apply the octahedron recurrence. Under the matching condition \[ \frac{u}{w^2}=\frac{u'}{(w')^2}, \] we prove that the resulting hive law is close, in relative entropy, to a GUE hive law. More precisely, if \[ a^2=w^2+u^2,\qquad b^2=(w')^2+(u')^2, \] then the produced hive density $q_n$ satisfies \[ D_{\mathrm{KL}}\!\left( q_n\, \middle\|\, \operatorname{Density}\bigl(H_n(a\sqrt n,b\sqrt n,c_{**}\sqrt n)\bigr) \right) = O(n\log n). \] The third scale $c_{**}$ is determined by a limiting tetrahedral optimization problem; equivalently, writing \(δ=u+u'\), \[ δ^2 = \frac{ 2c_{**}^4(c_{**}^2-a^2-b^2) }{ (c_{**}^2-a^2+b^2)(c_{**}^2+a^2-b^2) }. \] Thus the construction realizes GUE hive laws, up to subleading relative entropy, throughout the right-angled and obtuse regime. The introduction records two explicit surface-tension approximations and numerical comparisons which motivated the construction.
