惯性聚合 高效追踪和阅读你感兴趣的博客、新闻、科技资讯
阅读原文 在惯性聚合中打开

推荐订阅源

博客园 - 叶小钗
爱范儿
爱范儿
WordPress大学
WordPress大学
Last Week in AI
Last Week in AI
博客园 - 聂微东
雷峰网
雷峰网
奇客Solidot–传递最新科技情报
奇客Solidot–传递最新科技情报
博客园 - 三生石上(FineUI控件)
T
Tailwind CSS Blog
博客园 - Franky
酷 壳 – CoolShell
酷 壳 – CoolShell
博客园_首页
OSCHINA 社区最新新闻
OSCHINA 社区最新新闻
博客园 - 司徒正美
月光博客
月光博客
大猫的无限游戏
大猫的无限游戏
钛媒体:引领未来商业与生活新知
钛媒体:引领未来商业与生活新知
freeCodeCamp Programming Tutorials: Python, JavaScript, Git & More
The Cloudflare Blog
让小产品的独立变现更简单 - ezindie.com
让小产品的独立变现更简单 - ezindie.com
人人都是产品经理
人人都是产品经理
宝玉的分享
宝玉的分享
罗磊的独立博客
Jina AI
Jina AI

stat updates on arXiv.org

Simultaneous Monitoring of Shape and Surface Color via 4D Point Clouds: A Registration-free Approach A Refined Generalization Analysis for Extreme Multi-class Supervised Contrastive Representation Learning Ensemble Distributionally Robust Bayesian Optimisation The Proxy Presumption: From Semantic Embeddings to Valid Social Measures Modulated learning for private and distributed regression with just a single sample per client device Query-efficient model evaluation using cached responses Functional-prior-based approaches to Bayesian PDE-constrained inversion using physics-informed neural networks Optimal Experiments for Partial Causal Effect Identification Order-Agnostic Autoregressive Modelling with Missing Data Grokking or Glitching? How Low-Precision Drives Slingshot Loss Spikes Tuning Derivatives for Causal Fairness in Machine Learning Spherical Flows for Sampling Categorical Data Bayesian Rain Field Reconstruction using Commercial Microwave Links and Diffusion Model Priors GRALIS: A Unified Canonical Framework for Linear Attribution Methods via Riesz Representation Sharp Capacity Thresholds in Linear Associative Memory: From Winner-Take-All to Listwise Retrieval Unified Framework of Distributional Regret in Multi-Armed Bandits and Reinforcement Learning Jacobian-Velocity Bounds for Deployment Risk Under Covariate Drift Self-Attention as Transport: Limits of Symmetric Spectral Diagnostics Perturbation is All You Need for Extrapolating Language Models Adapt or Forget: Provable Tradeoffs Between Adam and SGD in Nonstationary Optimization Realizable Bayes-Consistency for General Metric Losses Graph Convolutional Support Vector Regression for Robust Spatiotemporal Forecasting of Urban Air Pollution Segmenting Human-LLM Co-authored Text via Change Point Detection Stochastic Schrödinger Diffusion Models for Pure-State Ensemble Generation Understanding Self-Supervised Learning via Latent Distribution Matching The Geometric Mechanics of Contrastive Representation Learning: Alignment Potentials, Entropic Dispersion, and Cross-modal Divergence Imbalanced Classification under Capacity Constraints On the Spectral Structure and Objective Equivalence of Orthogonal Multilabel Fisher Discriminants Partially Observed Structural Causal Models First-Order Efficiency for Probabilistic Value Estimation via A Statistical Viewpoint
Comparison theorems for the extreme eigenvalues of a rand...
[Submitted on 4 Mar 2026 (v1), last revised 5 Jul 2026 (this ver · 2026-03-05 · via stat updates on arXiv.org

View PDF HTML (experimental)

Abstract:This paper establishes a comparison theorem for the maximum eigenvalue of a sum of independent random symmetric matrices. The theorem states that the maximum eigenvalue of the matrix sum is dominated by the maximum eigenvalue of a Gaussian random matrix whose statistics match the sum, and it strengthens previous results of this type. Corollaries address the minimum eigenvalue and the spectral norm; the proof strategy also extends to matrix martingale sequences.
The comparison methodology is powerful because of the vast arsenal of tools for treating Gaussian random matrices. As applications, the paper improves on existing eigenvalue bounds for random matrices arising in spectral graph theory, quantum information theory, high-dimensional statistics, and numerical linear algebra. In particular, these techniques deliver the first complete proof that a sparse random dimension reduction map has the injectivity properties conjectured by Nelson & Nguyen in 2013.

Submission history

From: Joel Tropp [view email]
[v1] Wed, 4 Mar 2026 18:30:04 UTC (121 KB)
[v2] Sat, 14 Mar 2026 18:12:03 UTC (117 KB)
[v3] Sun, 5 Jul 2026 00:09:16 UTC (164 KB)