Tootfinder

Conditional central limit theorems for exponential random graphs
Xiao Fang, Song-Hao Liu, Zhonggen Su, Xiaolin Wang
https://arxiv.org/abs/2506.15159 https:…

Conditional central limit theorems for exponential random graphs
In this paper, we study the Exponential Random Graph Models (ERGMs) conditioning on the number of edges. In subcritical region of model parameters, we prove a conditional Central Limit Theorem (CLT) with explicit mean and variance for the number of two stars. This generalizes the corresponding result in the literature for the Erdős--Rényi random graph. To prove our main result, we develop a new conditional CLT via exchangeable pairs based on the ideas of Dey and Terlov. Our key technical cont…

A Parareal Algorithm with Spectral Coarse Solver
Martin J. Gander, Mario Ohlberger, Stephan Rave
https://arxiv.org/abs/2508.08873 https://arxiv.org/pdf/250…

A Parareal Algorithm with Spectral Coarse Solver
We consider a new class of Parareal algorithms, which use ideas from localized reduced basis methods to construct the coarse solver from spectral approximations of the transfer operators mapping initial values for a given time interval to the solution at the end of the interval. By leveraging randomized singular value decompositions, these spectral approximations are obtained embarrassingly parallel by computing local fine solutions for random initial values. We show a priori and a posteriori e…

Volume Entropy Rigidity for Random Groups at Low Densities
Dongming Hua (Merrick)
https://arxiv.org/abs/2505.23364 https://arxiv.org/…

Volume Entropy Rigidity for Random Groups at Low Densities
We study the rigidity of the volume entropy for weighted word metrics on hyperbolic groups, building on a recent convexity result due to Cantrell-Tanaka. Using ideas from small cancellation theory, we give conditions under which a hyperbolic group admits a unique normalized weight minimizing the entropy. Moreover, we show that these conditions are generic for random groups at small densities, and that the unique minimizer of such a generic group is arbitrarily close to the uniform weight.

Entropic additive energy and entropy inequalities for sums and products
Rupert Li, Lampros Gavalakis, Ioannis Kontoyiannis
https://arxiv.org/abs/2506.20813

Entropic additive energy and entropy inequalities for sums and products
Following a growing number of studies that, over the past 15 years, have established entropy inequalities via ideas and tools from additive combinatorics, in this work we obtain a number of new bounds for the differential entropy of sums, products, and sum-product combinations of continuous random variables. Partly motivated by recent work by Goh on the discrete entropic version of the notion of "additive energy", we introduce the additive energy of pairs of continuous random variables and prov…

Detecting non-uniform patterns on high-dimensional hyperspheres
Tiefeng Jiang, Tuan Pham
https://arxiv.org/abs/2506.00444 https://arx…

Detecting non-uniform patterns on high-dimensional hyperspheres
We propose a new probabilistic characterization of the uniform distribution on hyperspheres in terms of its inner product, extending the ideas of \cite{cuesta2009projection,cuesta2007sharp} in a data-driven manner. Using this characterization, we define a new distance that quantifies the deviation of an arbitrary distribution from uniformity. As an application, we construct a novel nonparametric test for the uniformity testing problem: determining whether a set of \(n\) i.i.d. random points on …

Ergodicity of the hard-core PCA with a random walk method
J\'er\^ome Casse, Ir\`ene Marcovici, Maxence Poutrel
https://arxiv.org/abs/2506.18632 https:/…

Ergodicity of the hard-core PCA with a random walk method
The hard-core probabilistic cellular automaton has attracted a renewed interest in the last few years, thanks to its connection with the study of a combinatorial game on percolation configurations. We provide an alternative proof for the ergodicity of this PCA for a neighbourhood of size $2$ and $3$, using the notion of decorrelated islands introduced by Casse in 2023, together with some new ideas. This shortens the previous proofs and provides a more intuitive and unified approach.