随机正则图上弱Anderson无序的固定能量普适性

随机正则图上弱Anderson无序的固定能量普适性

Fixed-energy universality for weak Anderson disorder on random regular graphs

OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。

具体内容

稿件研究均匀随机简单标记d-正则图（d≥3）邻接矩阵在独立均匀对角无序下的谱统计。摘要表示，对每个固定能量（位于干净谱带紧子区间内），当无序强度为正、充分小且随图增长固定时，重标度后的完整微观本征值点过程收敛到GOE体过程，重标度因子为相应无限树算子的正态密度。作者声称允许的无序强度依赖于度数与到干净谱边的距离。该结果属于随机矩阵与无序系统谱理论交叉方向；当前收录摘要未给出证明细节。

• 研究对象为随机d-正则图邻接矩阵加对角无序的谱统计。
• 作者声称固定能量处微观本征值点过程收敛到GOE体过程。
• 允许的无序强度依赖度数与到干净谱边的距离。

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英文原始摘要

For every fixed degree d ≥ 3, we prove fixed-energy GOE universality for the adjacency matrix of a uniformly random simple labelled d-regular graph with independent uniform diagonal disorder. The disorder strength is positive, sufficiently small, and fixed as the graph grows. At each fixed energy in a compact subinterval of the clean spectral band, the full microscopic eigenvalue point process converges to the GOE bulk process after rescaling by the positive density of states of the corresponding infinite-tree operator. The permitted disorder strength depends on the degree and the distance from the clean spectral edges.

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