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

D
DataBreaches.Net
IT之家
IT之家
博客园_首页
博客园 - 【当耐特】
V
V2EX
Apple Machine Learning Research
Apple Machine Learning Research
G
Google Developers 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
Recent Announcements
Recent Announcements
F
Fortinet All Blogs
GbyAI
GbyAI
腾讯CDC
H
Hackread – Cybersecurity News, Data Breaches, AI and More
OSCHINA 社区最新新闻
OSCHINA 社区最新新闻
I
InfoQ
H
Help Net Security
T
Tailwind CSS Blog
B
Blog RSS Feed
Martin Fowler
Martin Fowler
人人都是产品经理
人人都是产品经理
The Cloudflare Blog
博客园 - 叶小钗
雷峰网
雷峰网
量子位

math.PR updates on arXiv.org

Visibility in the Boolean Model on Harmonic Manifolds Global estimates on the Brenier map Geodesics and Wandering Exponents in Brochette First-Passage Percolation State-dependent inverse-subordinator time changes of regenerative processes: Excursion structure and multiscale occupation-time limits Randomly twisted transfer operators and singular values statistics Generalized Bessel-Dunkl diffusions An almost sure invariance principle for the Takagi-van der Waerden class functions Central limit theorems for high dimensional lattice polytopes: cosmological polytopes Convergence rate estimates for semigroups and heat kernels associated with resistance forms Second-order Poincaré inequalities and localization on the Poisson space Maximum Probability of Independence in Transitive Matroids On global solutions to the semidiscrete stochastic heat equation The Poisson Tail Conjecture for primes in short intervals A Complete Spectral Analysis of the CEV Operator with Applications to Arbitrage Holographic functions and neural networks From Betting to Empirical Bernstein LIL Concentration of General Stochastic Approximation Under Heavy-Tailed Markovian Noise Pointwise Generalization in Deep Neural Networks Bayesian Latent Space Models for Graphs Are Misspecified: Toward Robust Inference via Generalized Posteriors Wasserstein bounds for denoising diffusion probabilistic models via the Föllmer process A note on connections between the Föllmer process and the denoising diffusion probabilistic model Simple Approximation and Derivative Free Inference-Time Scaling for Diffusion Models via Sequential Monte Carlo on Path Measures Diffusion-Based Stochastic Operator Networks for Uncertainty Quantification in Stochastic Partial Differential Equations A Fourier perspective on the learning dynamics of neural networks: from sample complexities to mechanistic insights Propagation of Chaos in Contextual Flow Maps Dimension-Uniform Discretization Analysis of Preconditioned Annealed Langevin Dynamics for Multimodal Gaussian Mixtures $α$-TCAV: A Unified Framework for Testing with Concept Activation Vectors Scaling Laws from Sequential Feature Recovery: A Solvable Hierarchical Model On the Limits of Latent Reuse in Diffusion Models State-of-art minibatches via novel DPP kernels: discretization, wavelets, and rough objectives
Delocalization of a general class of random block Schrödi...
Fan Yang, Jun Yin · 2025-01-15 · via math.PR updates on arXiv.org

We consider a natural class of extensions of the Anderson model on $\mathbb Z^d$, called random block Schrödinger operators (RBSOs), defined on the $d$-dimensional torus $(\mathbb Z/L\mathbb Z)^d$. These operators take the form $H=V+λΨ$, where $V$ is a diagonal block matrix whose diagonal blocks are i.i.d. $W^d\times W^d$ GUE, representing a random block potential, $Ψ$ describes interactions between neighboring blocks, and $λ\ll 1$ is a small coupling parameter (making $H$ a perturbation of $V$). We focus on three specific RBSOs: (1) the block Anderson model, where $Ψ$ is the discrete Laplacian on $(\mathbb Z/L\mathbb Z)^d$; (2) the Anderson orbital model, where $Ψ$ is a block Laplacian operator; (3) the Wegner orbital model, where the nearest-neighbor blocks of $Ψ$ are themselves random matrices. Assuming $d\ge 7$ and $W\ge L^\varepsilon$ for a small constant $\varepsilon>0$, and under a certain lower bound on $λ$, we establish delocalization and quantum unique ergodicity for bulk eigenvectors, along with quantum diffusion estimates for the Green's function. Combined with the localization results of arXiv:1608.02922, our results rigorously demonstrate the existence of an Anderson localization-delocalization transition for RBSOs as $λ$ varies. Our proof is based on the $T$-expansion method and the concept of self-energy renormalization, originally developed in the study of random band matrices in arXiv:2104.12048. In addition, we introduce a conceptually novel idea, called coupling renormalization, which extends the notion of self-energy renormalization. While this phenomenon is well-known in quantum field theory, it is identified here for the first time in the context of random Schrödinger operators. We expect that our methods can be extended to models with real or non-Gaussian block potentials, as well as more general forms of interactions.