Related papers: Stein's method and a cubic mean-field model
We study a mean-field spin model with three- and two-body interactions. The equilibrium measure for large volumes is shown to have three pure states, the phases of the model. They include the two with opposite magnetization and an…
This paper establishes a non-uniform Berry--Esseen bound in normal approximation for exchangeable pairs using Stein's method via a concentration inequality approach. The main theorem extends and improves several results in the literature,…
We obtain rates of convergence in limit theorems of partial sums $S_n$ for certain sequences of dependent, identically distributed random variables, which arise naturally in statistical mechanics, in particular, in the context of the…
An exchangeable pair approach is commonly taken in the normal and non-normal approximation using Stein's method. It has been successfully used to identify the limiting distribution and provide an error of approximation. However, when the…
This paper establishes a non-uniform Berry--Esseen bound for non-normal approximation using Stein's method. The main theorem generalizes the result of the authors in [Comptes Rendus Mathematique, 2024] to the context of non-normal…
Limit theorems for the magnetization in the $p$-spin Curie-Weiss model, for $p \geq 3$, has been derived recently by Mukherjee et al. (2021). In this paper, we strengthen these results by proving Cram\'er-type moderate deviation theorems…
We study a block spin mean-field Ising model, i.e. a model of spins in which the vertices are divided into a finite number of blocks with each block having a fixed proportion of vertices, and where pair interactions are given according to…
We study the inhomogeneous Curie-Weiss model with external field, where the inhomogeneity is introduced by adding a positive weight to every vertex and letting the interaction strength between two vertices be proportional to the product of…
Stein's method for concentration inequalities was introduced to prove concentration of measure in problems involving complex dependencies such as random permutations and Gibbs measures. In this paper, we provide some extensions of the…
We analyze in some detail a recently proposed transfer matrix mean field approximation which yields the exact critical point for several two dimensional nearest neighbor Ising models. For the square lattice model we show explicitly that…
Although the fully connected Ising model does not have a length scale, we show that its critical exponents can be found using finite size scaling with the scaling variable equal to N, the number of spins. We find that at the critical…
Applying an inductive technique for Stein and zero bias couplings yields Berry-Esseen theorems for normal approximation for two new examples. The conditions of the main results do not require that the couplings be bounded. Our two…
We study the distribution of the magnetization of the critical mean-field O(N) model with N > 1. Specifically, we bound the Wasserstein distance between the finite-volume and limiting distributions, in terms of the number of spins. To…
The bulk and boundary magnetizations are calculated for the critical Ising model on a randomly triangulated disk in the presence of a boundary magnetic field h. In the continuum limit this model corresponds to a c = 1/2 conformal field…
Concentration inequalities for the sample mean, like those due to Bernstein, Hoeffding, and Bentkus, are valid for any sample size but overly conservative, yielding confidence intervals that are unnecessarily wide. The central limit theorem…
Important gaps remain in our understanding of the thermodynamics and statistical physics of self-gravitating systems. Using mean field theory, here we investigate the equilibrium properties of several spherically symmetric model systems…
Using a modification of Stein's method, we generalize the results of Bentkus, G{\"o}tze, and Tikhomirov \cite{bentkus1997berry} to obtain Berry-Esseen bounds for a broad class of statistics of sequences of $\phi$-mixing, non-stationary…
We establish central limit theorems for a large class of supercritical branching Markov processes in infinite dimension with spatially dependent and non-necessarily local branching mechanisms. This result relies on a fourth moment…
This paper studies the rate of convergence of a family of continuous-time Markov chains (CTMC) to a mean-field model. When the mean-field model is a finite-dimensional dynamical system with a unique equilibrium point, an analysis based on…
In this paper, a new technique is introduced to obtain non-uniform Berry-Esseen bounds of normal and nonnormal approximation for unbounded exchangeable pairs. This technique does not rely on the concentration inequalities developed by Chen…