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_首页
Y
Y Combinator Blog
Engineering at Meta
Engineering at Meta
D
Docker
GbyAI
GbyAI
aimingoo的专栏
aimingoo的专栏
大猫的无限游戏
大猫的无限游戏
腾讯CDC
P
Proofpoint News Feed
A
About on SuperTechFans
WordPress大学
WordPress大学
Stack Overflow Blog
Stack Overflow Blog
Google DeepMind News
Google DeepMind News
C
Check Point Blog
Microsoft Security Blog
Microsoft Security Blog
H
Hackread – Cybersecurity News, Data Breaches, AI and More
L
LangChain Blog
MyScale Blog
MyScale Blog
博客园 - 三生石上(FineUI控件)
Hugging Face - Blog
Hugging Face - Blog
Microsoft Azure Blog
Microsoft Azure Blog
N
Netflix TechBlog - Medium
G
Google Developers Blog
OSCHINA 社区最新新闻
OSCHINA 社区最新新闻

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
Fluctuations in Various Regimes of Non-Hermiticity and a ...
G. Akemann, M. Duits, L. D. Molag · 2024-12-20 · via math.PR updates on arXiv.org

The variance of the number of particles in a set is an important quantity in understanding the statistics of non-interacting fermionic systems in low dimensions. An exact map of their ground state in a harmonic trap in one and two dimensions to the classical Gaussian unitary and complex Ginibre ensemble, respectively, allows to determine the counting statistics at finite and infinite system size. We will establish two new results in this setup. First, we uncover an interpolating central limit theorem between known results in one and two dimensions, for linear statistics of the elliptic Ginibre ensemble. We find an entire range of interpolating weak non-Hermiticity limits, given by a two-parameter family for the mesoscopic scaling regime. Second, we considerably generalize the proportionality between the number variance and the entanglement entropy between Fermions in a set $A$ and its complement in two dimensions. Previously known only for rotationally invariant sets and external potentials, we prove a holographic principle for general non-rotationally invariant sets and random normal matrices. It states that both number variance and entanglement entropy are proportional to the circumference of $A$.