AI 中文总结
该研究针对随机形变高斯酉系综的最大特征值，推导了其在固定耦合 regime 下左右尾的精确对数渐近及相图，建立了一致的Airy近似并结合条件卷积论证完成分析。
AI 中文摘要
我们研究由Johansson（Probab. Theory Relat. Fields, {\bf 138}: 75--112, 2007）引入的随机形变高斯酉系综最大特征值的中偏差。在固定耦合 regime 下，重标后的最大特征值收敛于Tracy--Widom律与谱边随机位移产生的高斯律的卷积。我们在增长的Airy尺度上推导了左右尾的精确对数渐近，并得到了相应的相图。两个尾部具有不同的转变尺度。在临界点，速率函数是Tracy--Widom速率函数与高斯速率函数的非平凡下卷积。我们建立了迹范数Airy近似，该近似在对数窗口内对典型对角构型是一致的。随后，通过条件卷积论证，将所得尾估计与谱边位移的高斯中偏差相结合。
英文摘要
We study moderate deviations for the largest eigenvalue of the randomly deformed Gaussian unitary ensemble introduced by Johansson (Probab. Theory Relat. Fields, {\bf 138}: 75--112, 2007). In the fixed-coupling regime, the rescaled largest eigenvalue converges to the convolution of the Tracy--Widom law and a Gaussian law arising from the random displacement of the spectral edge. We derive sharp logarithmic asymptotics for the right and left tails on growing Airy scales and obtain the corresponding phase diagram. The two tails have different transition scales. At criticality, the rate functions are nontrivial infimal convolutions of the Tracy--Widom and Gaussian rate functions. We establish a trace-norm Airy approximation that is uniform over typical diagonal configurations on a logarithmic window. A conditional convolution argument then combines the resulting tail estimates with the Gaussian moderate deviations of the edge displacement.
CommentsComments are welcome; 36 pages, 2 figures
