AI & ML
Tracy Widom law for sample covariance matrices under quadratic form concentration
arXiv stat.TH0 views
arXiv:2610.41416v1 Announce Type: cross Abstract: We study sample covariance matrices formed from i.i.d., centered, isotropic random vectors $q_1, \dots, q_N \in \mathbb{R}^M$, whose coordinates are allowed to be dependent. We assume the random vectors satisfy a concentration bound for their quadratic forms $q_i^T A q_i$. Under this assumption, we establish edge universality and obtain the Tracy--Widom law for the largest eigenvalue of the sample covariance matrix after appropriate centering and scaling. In particular, our result removes the unconditionality assumption in existing edge universality results for log-concave ensembles~\cite{BX}, resolving the question that originally motivated our work. The concentration assumption also allows us to extend the result beyond the log-concave class.
Source:https://arxiv.org/abs/2610.41416PreviousTruthful and Admissible Principal--Agent Testing with Nuisance ParametersNextUncertainty Quantification for Topological Treatment Effects
Related posts

Agents draft. People decide.
0dev.to UX

โค้ดเพิ่ม 400% แต่คุณไม่ได้เร็วขึ้น 400%: GitHub ชี้คอขวดใหม่อยู่ที่การรีวิว
0dev.to GitHub

Drago: Your GitHub Dragon
0dev.to GitHub
Case Study: Automating Tableau to Power BI Migration with Up to 90% Accuracy.
0dev.to Data
Vom Bluttest ins Molekül: Warum die Alamar/Nightingale-Studie räumliches Denken braucht...
0dev.to Data
10x Genomics가 Anthropic의 Claude AI를 Chromium 플랫폼에 통합한 'Sentira'를 발표했습니다. 단일세포 데이터 분석을 가...
0dev.to Data