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We consider a class of non-conformal expanding maps on the $d$-dimensional torus. For an equilibrium measure of an H\"older potential, we prove an analogue of the Central Limit Theorem for the fluctuations of the logarithm of the measure of…

Dynamical Systems · Mathematics 2009-12-17 Renaud Leplaideur , Benoit Saussol

This paper proves limit theorems for the number of monochromatic edges in uniform random colorings of general random graphs. These can be seen as generalizations of the birthday problem (what is the chance that there are two friends with…

Probability · Mathematics 2018-02-13 Bhaswar B. Bhattacharya , Persi Diaconis , Sumit Mukherjee

We review and present some known results for non-linear functionals of Gaussian variables in the context of discrete Gaussian fields defined on the $d$ dimensional lattice. Our main result is a Central Limit Theorem in the spirit of the…

Probability · Mathematics 2025-12-16 Fabio Coppini , Wioletta M. Ruszel

In the paper [25], written in collaboration with Gesine Reinert, we proved a universality principle for the Gaussian Wiener chaos. In the present work, we aim at providing an original example of application of this principle in the…

Probability · Mathematics 2010-02-08 Ivan Nourdin , Giovanni Peccati

The present paper extends the results on the ferromagnetic Dyson models from \cites{EFMV2024, JOP2025} to the near-critical and strongly interacting regimes. As part of our main result, we further establish Gaussian concentration bounds for…

Probability · Mathematics 2025-08-05 Mirmukhsin Makhmudov

Many low temperature disordered systems are expected to exhibit Poisson-Dirichlet (PD) statistics. In this paper, we focus on the case when the underlying disorder is a logarithmically correlated Gaussian process $\phi_N$ on the box…

Probability · Mathematics 2023-02-15 Shirshendu Ganguly , Kyeongsik Nam

We consider the Grenander estimator that is the maximum likelihood estimator for non-increasing densities. We prove uniform central limit theorems for certain subclasses of bounded variation functions and for H\"older balls of smoothness…

Statistics Theory · Mathematics 2015-06-29 Jakob Söhl

The exponential random graph model (ERGM) is a central object in the study of clustering properties in social networks as well as canonical ensembles in statistical physics. Despite some breakthrough works in the mathematical understanding…

Probability · Mathematics 2021-08-06 Shirshendu Ganguly , Kyeongsik Nam

We present a general result which shows that the winding of the branches in a uniform spanning tree on a planar graph converge in the limit of fine mesh size to a Gaussian free field. The result holds true assuming only convergence of…

Probability · Mathematics 2018-11-28 Nathanaël Berestycki , Benoit Laslier , Gourab Ray

We study the second-order asymptotics around the superdiffusive strong law~\cite{MMW} of a multidimensional driftless diffusion with oblique reflection from the boundary in a generalised parabolic domain. In the unbounded direction we prove…

Probability · Mathematics 2024-12-20 Aleksandar Mijatović , Isao Sauzedde , Andrew Wade

We consider the edge-triangle model, a two-parameter family of exponential random graphs in which dependence between edges is introduced through triangles. In the so-called replica symmetric regime, the limiting free energy exists together…

Probability · Mathematics 2023-01-31 Alessandra Bianchi , Francesca Collet , Elena Magnanini

We consider a class of self-similar, continuous Gaussian processes that do not necessarily have stationary increments. We prove a version of the Breuer-Major theorem for this class, that is, subject to conditions on the covariance function,…

Probability · Mathematics 2016-12-06 Daniel Harnett , David Nualart

We present a general approach to establish the Central Limit Theorem with error bounds for sequential dynamical systems. The main tool we develop is the application to this setting of a projective metric on complex cones, following the…

Dynamical Systems · Mathematics 2025-07-21 Mark F. Demers , Carlangelo Liverani

We address the issue of the Central Limit Theorem for (both local and global) empirical measures of diffusions interacting on a possibly diluted Erd\H{o}s-R\'enyi graph. Special attention is given to the influence of initial condition (not…

Probability · Mathematics 2022-08-11 Fabio Coppini , Eric Luçon , Christophe Poquet

We prove that for q>=1, there exists r(q)<1 such that for p>r(q), the number of points in large boxes which belongs to the infinite cluster has a normal central limit behaviour under the random cluster measure phi_{p,q} on Z^d, d>=2.…

Probability · Mathematics 2007-05-23 Olivier Garet

We focus on the FeigenbaumCoulletTresser point of the dissipative one-dimensional z logistic map. We show that sums of iterates converge to q Gaussian distributions, which optimize the nonadditive entropic functional Sq under simple…

Statistical Mechanics · Physics 2025-08-20 Abbas Ali Saberi , Ugur Tirnakli , Constantino Tsallis

Central limit theorems for linear statistics of lattice random fields (including spin models) are usually proven under suitable mixing conditions or quasi-associativity. Many interesting examples of spin models do not satisfy mixing…

Probability · Mathematics 2018-03-28 Tulasi Ram Reddy , Sreekar Vadlamani , D. Yogeshwaran

We consider a class of Gibbs measures defined with respect to increments $\{\omega(t)-\omega(s)\}_{s<t}$ of $d$-dimensional Wiener measure, with the underlying Hamiltonian carrying interactions of the form $H(t-s,\omega(t)-\omega(s))$ that…

Probability · Mathematics 2021-07-27 Chiranjib Mukherjee

We prove a Central Limit Theorem for probability measures defined via the variation of the sum-of-digits function, in base $b\ge 2$. For $r\ge 0$ and $d \in \mathbb{Z}$, we consider $\mu^{(r)}(d)$ as the density of integers $n\in…

Probability · Mathematics 2024-03-14 Yohan Hosten , Élise Janvresse , Thierry de la Rue

A discrete gradient model for interfaces is studied. The interaction potential is a non-convex perturbation of the quadratic gradient potential. Based on a representation for the finite volume Gibbs measure obtained via a renormalization…

Mathematical Physics · Physics 2016-03-16 Susanne Hilger