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

G
Google Developers Blog
云风的 BLOG
云风的 BLOG
Google DeepMind News
Google DeepMind News
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
博
博客园 - 三生石上(FineUI控件)
V
Visual Studio Blog
爱范儿
爱范儿
宝玉的分享
宝玉的分享
人人都是产品经理
人人都是产品经理
大猫的无限游戏
大猫的无限游戏
博
博客园 - 聂微东
月光博客
月光博客
雷峰网
雷峰网
L
LangChain Blog
Stack Overflow Blog
Stack Overflow Blog
B
Blog RSS Feed
有赞技术团队
有赞技术团队
T
Tailwind CSS Blog
阮一峰的网络日志
阮一峰的网络日志
V
V2EX
CTFtime.org: upcoming CTF events
CTFtime.org: upcoming CTF events
C
Check Point Blog
N
Netflix TechBlog - Medium
罗
罗磊的独立博客
博
博客园 - 司徒正美
OSCHINA 社区最新新闻
OSCHINA 社区最新新闻
F
Full Disclosure
Security Archives - TechRepublic
Security Archives - TechRepublic
V
Vulnerabilities – Threatpost
H
Help Net Security
博
博客园 - 【当耐特】
博
博客园_首页
Microsoft Security Blog
Microsoft Security Blog
小众软件
小众软件
Hugging Face - Blog
Hugging Face - Blog
L
Lohrmann on Cybersecurity
C
Cybersecurity and Infrastructure Security Agency CISA
P
Privacy International News Feed
Blog — PlanetScale
Blog — PlanetScale
C
CERT Recently Published Vulnerability Notes
P
Privacy & Cybersecurity Law Blog
酷 壳 – CoolShell
酷 壳 – CoolShell
Cisco Talos Blog
Cisco Talos Blog
K
Kaspersky official blog
D
Darknet – Hacking Tools, Hacker News & Cyber Security
Cyberwarzone
Cyberwarzone
S
Schneier on Security
S
SegmentFault 最新的问题
C
Cyber Attacks, Cyber Crime and Cyber Security
S
Securelist

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 A Unified Framework for Critical Scaling of Inverse Temperature in Self-Attention Expected Batch Optimal Transport Plans and Consequences for Flow Matching Partial Model Sharing Improves Byzantine Resilience in Federated Conformal Prediction GRAFT-ATHENA: Self-Improving Agentic Teams for Autonomous Discovery and Evolutionary Numerical Algorithms Uniform Scaling Limits in AdamW-Trained Transformers Constant-Target Energy Matching: A Unified Framework for Continuous and Discrete Density Estimation Scaling Limits of Long-Context Transformers Generalized Wasserstein Flow Matching: Transport Plans, Everywhere, All at Once Convergence Analysis of Newton's Method for Neural Networks in the Overparameterized Limit Convergent Stochastic Training of Attention and Understanding LoRA Universality of the fluctuations of the free energy in generalized Sherrington-Kirkpatrick models and the log likelihood ratio in spiked Wigner models Expressivity of Bi-Lipschitz Normalizing Flows: A Score-Based Diffusion Perspective Time-Inhomogeneous Preconditioned Langevin Dynamics Matrix-Decoupled Concentration for Autoregressive Sequences: Dimension-Free Guarantees for Sparse Long-Context Rewards Convex-Geometric Error Bounds for Positive-Weight Kernel Quadrature Variational Smoothing and Inference for SDEs from Sparse Data with Dynamic Neural Flows Grokability in five inequalities Almost-Orthogonality in Lp Spaces: A Case Study with Grok On Computing Total Variation Distance Between Mixtures of Product Distributions Universality in Deep Neural Networks: An approach via the Lindeberg exchange principle Soft-to-Hard Routing in Sparse Mixture-of-Experts Models Learning Discriminators for Resampling in the Ensemble Gaussian Mixture Filter through a Normalizing Flow Approach Decentralized Proximal Stochastic Gradient Langevin Dynamics A Review of the Receiver Operating Characteristic Curve and a Proof About the Area Beneath It Stochastic Scaling Limits and Synchronization by Noise in Deep Transformer Models Well-Conditioned Oblivious Perturbations in Linear Space Mathematical Foundations for Peer-to-Peer Lattice Computation Achieving the Kesten-Stigum bound in the non-uniform hypergraph stochastic block model Phase Transitions in the Fluctuations of Functionals of Random Neural Networks Ultrametric OGP - parametric RDT \emph{symmetric} binary perceptron connection Geometric regularization of autoencoders via observed stochastic dynamics A Wasserstein Geometric Framework for Hebbian Plasticity Neural Continuous-Time Markov Chain: Discrete Diffusion via Decoupled Jump Timing and Direction One-Shot Generative Flows: Existence and Obstructions Wasserstein Formulation of Reinforcement Learning. An Optimal Transport Perspective on Policy Optimization node2vec or triangle-biased random walks: stationarity, regularity & recurrence Some Theoretical Limitations of t-SNE Adaptive Learning via Off-Model Training and Importance Sampling for Fully Non-Markovian Optimal Stochastic Control. Complete version Tail-Aware Information-Theoretic Generalization for RLHF and SGLD Diffusion Processes on Implicit Manifolds Degrees, Levels, and Profiles of Contextuality High-accuracy log-concave sampling with stochastic queries Variational Optimality of Föllmer Processes in Generative Diffusions Diffusion Model's Generalization Can Be Characterized by Inductive Biases toward a Data-Dependent Ridge Manifold Dimension-Free Multimodal Sampling via Preconditioned Annealed Langevin Dynamics A Review of Diffusion-based Simulation-Based Inference: Foundations and Applications in Non-Ideal Data Scenarios Feature Learning Dynamics in Infinite-Depth Neural Networks On The Hidden Biases of Flow Matching Samplers Fast and Robust Diffusion Posterior Sampling for MR Image Reconstruction Using the Preconditioned Unadjusted Langevin Algorithm Normalizing Flows on Quotient Manifolds via Boundary Quotients Differentiable Filtering for Learning Hidden Markov Models Limit Theorems for Stochastic Gradient Descent in High-Dimensional Single-Layer Networks Posterior Bayesian Neural Networks with Dependent Weights Exponentially Fading Memory Signature A decision-theoretic approach to dealing with uncertainty in quantum mechanics On Statistical Estimation of Edge-Reinforced Random Walks Efficiency of Parallel and Restart Exploration Strategies in Model Free Stochastic Simulations The feasibility of multi-graph alignment: a Bayesian approach Gaussian Approximation and Multiplier Bootstrap for Stochastic Gradient Descent Mean-field limit from general mixtures of experts to quantum neural networks On an $L^2$ norm for stationary ARMA processes Mirror Descent-Ascent for mean-field min-max problems Universal approximation property of Banach space-valued random feature models including random neural networks Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for Kolmogorov partial differential equations with Lipschitz nonlinearities in the $L^p$-sense Conditional stochastic differential equations driven by fractional Brownian motion Large deviations for the mean-field limit of Hawkes processes Distribution-Free Stochastic Analysis and Robust Multilevel Vector Field Anomaly Detection Change of measure through the Legendre transform On quantitative Laplace-type convergence results for some exponential probability measures, with two applications Convergence rates for gradient descent in the training of overparameterized artificial neural networks with piecewise affine activation
Stability and robustness of mathematical quasicrystals under statistical convergence
[Submitted on 22 Dec 2025 (v1), last revised 8 Jul 2026 (this ve · 2025-12-23 · via math.PR updates on arXiv.org

Mathematical Physics

arXiv:2512.19854 (math-ph)

[Submitted on 22 Dec 2025 (v1), last revised 8 Jul 2026 (this version, v2)]

View PDF

Abstract:In this work we address the stability and robustness of uniformly discrete point sets in Euclidean spaces. Firstly, we prove that if a sequence of point configurations contained in $\mathbb{R}^d$ is uniformly diffractive, converges rapidly enough to a discrete set $X$ in $\mathbb{R}^d$, and their diffraction measures $\widehat{\gamma_{X_n}}$ are asymptotically orthogonal with respect to the Lebesgue measure in $\mathbb{R}^d$, then $X$ is necessarily a quasicrystal. The convergence is addressed for a distance that quantifies the statistical closeness between two uniformly discrete point sets in $\mathbb{R}^d$. Secondly, motivated by their applications in the diffraction theory of quasicrystals, we establish the continuity of the Fourier Transform of quasicrystals in this topology. This continuity result, in turn, allows us to rigorously demonstrate that well-known robustness properties of quasicrystals against random errors remain stable under the statistical convergence considered. Some applications for rapidly-solidified quasicrystals are highlighted.
Comments: V1->V2. Changes in the exposition and introduction. We add more explanations regarding the FT of a quasicrystal. The continuity of the FT now appears as Thm B. We change the definition of unif. quas. by unif. diffractivity, to encompass a broader class of quasicrystals. 20->27 pages. Comments are welcome
Subjects: Mathematical Physics (math-ph); Functional Analysis (math.FA); Metric Geometry (math.MG); Probability (math.PR)
MSC classes: 52C23 (Primary), 42B10, 28C05
Cite as: arXiv:2512.19854 [math-ph]
  (or arXiv:2512.19854v2 [math-ph] for this version)
  https://doi.org/10.48550/arXiv.2512.19854

arXiv-issued DOI via DataCite

Submission history

From: Rodolfo Viera [view email]
[v1] Mon, 22 Dec 2025 20:15:15 UTC (25 KB)
[v2] Wed, 8 Jul 2026 15:03:31 UTC (28 KB)

Current browse context:

math-ph

Bookmark

BibSonomy Reddit

Bibliographic Tools

Bibliographic and Citation Tools

Bibliographic Explorer Toggle

Code, Data, Media

Code, Data and Media Associated with this Article

Demos

Demos

Related Papers

Recommenders and Search Tools

About arXivLabs

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。