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

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
MyScale Blog
MyScale Blog
U
Unit 42
M
MIT News - Artificial intelligence
小众软件
小众软件
P
Proofpoint News Feed
雷峰网
雷峰网
L
LangChain Blog
S
SegmentFault 最新的问题
腾讯CDC
F
Fortinet All Blogs
A
About on SuperTechFans
WordPress大学
WordPress大学
Vercel News
Vercel News
奇客Solidot–传递最新科技情报
奇客Solidot–传递最新科技情报
G
Google Developers Blog
大猫的无限游戏
大猫的无限游戏
OSCHINA 社区最新新闻
OSCHINA 社区最新新闻
D
Docker
N
Netflix TechBlog - Medium
Apple Machine Learning Research
Apple Machine Learning Research
Recent Announcements
Recent Announcements
D
DataBreaches.Net
Stack Overflow Blog
Stack Overflow Blog

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
The boundary of random planar maps via looptrees
Igor Kortchemski, Loïc Richier · 2018-02-02 · via math.PR updates on arXiv.org

We study the scaling limits of looptrees associated with Bienaymé--Galton--Watson (BGW) trees, that are obtained by replacing every vertex of the tree by a "cycle" whose size is its degree. First, we consider BGW trees whose offspring distribution is critical and in the domain of attraction of a Gaussian distribution. We prove that the Brownian CRT is the scaling limit of the associated looptrees, thereby confirming a prediction of [CK14b]. Then, we deal with BGW trees whose offspring distribution is critical and heavy-tailed. We show that the scaling limit of the associated looptrees is a multiple of the unit circle. This corresponds to a so-called condensation phenomenon, meaning that the underlying tree exhibits a vertex with macroscopic degree. Here, we rely on an invariance principle for random walks with negative drift, which is of independent interest. Finally, we apply these results to the study of the scaling limits of large faces of Boltzmann planar maps. We complete the results of [Ric17] and establish a phase transition for the topology of these maps in the non-generic critical regime.