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

大猫的无限游戏
大猫的无限游戏
阮一峰的网络日志
阮一峰的网络日志
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
WordPress大学
WordPress大学
博客园 - 叶小钗
Hugging Face - Blog
Hugging Face - Blog
博客园 - 司徒正美
Last Week in AI
Last Week in AI
罗磊的独立博客
量子位
Jina AI
Jina AI
T
Tailwind CSS Blog
Apple Machine Learning Research
Apple Machine Learning Research
IT之家
IT之家
美团技术团队
雷峰网
雷峰网
爱范儿
爱范儿
S
SegmentFault 最新的问题
小众软件
小众软件
月光博客
月光博客
酷 壳 – CoolShell
酷 壳 – CoolShell
人人都是产品经理
人人都是产品经理
The Cloudflare Blog
奇客Solidot–传递最新科技情报
奇客Solidot–传递最新科技情报

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
Coexistence, enhancements and short loops in random walk ...
Nicolas Forien, Matteo Quattropani, Alexandra Quitmann, Lorenzo · 2023-06-21 · via math.PR updates on arXiv.org

We consider a general random walk loop soup which includes, or is related to, several models of interest, such as the Spin O(N) model, the double dimer model and the Bose gas. The analysis of this model is challenging because of the presence of spatial interactions between the loops. For this model it is known from Quitmann and Taggi (2022) that macroscopic loops occur in dimension three and higher when the inverse temperature is large enough. Our first result is that, on the $d$ dimensional lattice, the presence of repulsive interactions is responsible for a shift of the critical inverse temperature, which is strictly greater than $\frac{1}{2d}$, the critical value in the non interacting case. Our second result is that a positive density of microscopic loops exists for all values of the inverse temperature. This implies that, in the regime in which macroscopic loops are present, microscopic and macroscopic loops coexist. Moreover, we show that, even though the increase of the inverse temperature leads to an increase of the total loop length, the density of microscopic loops is uniformly bounded from above in the inverse temperature. Our last result is confined to the special case in which the random walk loop soup is the one associated to the Spin O(N) model with arbitrary integer values of $N \geq 2$ and states that, on $\mathbb{Z}^2$, the probability that two vertices are connected by a loop decays at least polynomially fast with their distance.