English
Related papers

Related papers: A cram\'er type moderate deviation theorem for the…

200 papers

We derive moderate deviation principles for the trajectory of the empirical magnetization of the standard Curie-Weiss model via a general analytic approach based on convergence of generators and uniqueness of viscosity solutions for…

Probability · Mathematics 2017-10-13 Francesca Collet , Richard Kraaij

The random field Curie-Weiss model is derived from the classical Curie-Weiss model by replacing the deterministic global magnetic field by random local magnetic fields. This opens up a new and interestingly rich phase structure. In this…

Probability · Mathematics 2013-04-18 Matthias Löwe , Raphael Meiners

In Stein's method, the exchangeable pair approach is commonly used to estimate the approximation errors in normal approximation. In this paper, we establish a Cram\'er-type moderate deviation theorem of normal approximation for unbounded…

Probability · Mathematics 2022-09-26 Zhuo-Song Zhang

We establish Cram\'er-type moderate deviation theorems for sums of locally dependent random variables and combinatorial central limit theorems. Under some mild exponential moment conditions, optimal error bounds and convergence ranges are…

Probability · Mathematics 2021-12-22 Song-Hao Liu , Zhuo-Song Zhang

In the present paper we prove moderate deviations for a Curie-Weiss model with external magnetic field generated by a dynamical system, as introduced by Dombry and Guillotin-Plantard. The results extend those already obtained in the case of…

Probability · Mathematics 2011-07-05 Anselm Reichenbachs

Stein's method is applied to obtain a general Cramer-type moderate deviation result for dependent random variables whose dependence is defined in terms of a Stein identity. A corollary for zero-bias coupling is deduced. The result is also…

Probability · Mathematics 2013-02-06 Louis H. Y. Chen , Xiao Fang , Qi-Man Shao

Cram\'er type moderate deviation theorems quantify the accuracy of the relative error of the normal approximation and provide theoretical justifications for many commonly used methods in statistics. In this paper, we develop a new…

Probability · Mathematics 2016-06-07 Qi-Man Shao , Wen-Xin Zhou

We study a Curie-Weiss model with a random external field generated by a dynamical system. Probabilistic limit theorems (weak law of large numbers, central limit theorems) are proven for the corresponding magnetization.

Probability · Mathematics 2007-05-23 Clement Dombry , Nadine Guillotin-Plantard

We study the Cram\'er type moderate deviation for partial sums of random fields by applying the conjugate method. The results are applicable to the partial sums of linear random fields with short or long memory and to nonparametric…

Statistics Theory · Mathematics 2019-07-22 Aleksandr Beknazaryan , Hailin Sang , Yimin Xiao

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…

Probability · Mathematics 2024-03-22 Somabha Mukherjee , Tianyu Liu , Bhaswar B. Bhattacharya

In this paper, we establish normalized and self-normalized Cram\'er-type moderate deviations for Euler-Maruyama scheme for SDE. As a consequence of our results, Berry-Esseen's bounds and moderate deviation principles are also obtained. Our…

Probability · Mathematics 2023-05-19 Xiequan Fan , Haijuan Hu , Lihu Xu

The dynamical Curie-Weiss model of self-organized criticality (SOC) was introduced in \cite{Gor17} and it is derived from the classical generalized Curie-Weiss by imposing a microscopic Markovian evolution having the distribution of the…

Probability · Mathematics 2020-03-31 Francesca Collet , Matthias Gorny , Richard Clemens Kraaij

We analyze the dynamics of moderate fluctuations for macroscopic observables of the random field Curie Weiss model (i.e., standard Curie-Weiss model embedded in a site dependent, i.i.d. random environment). We obtain path space large…

Probability · Mathematics 2018-03-13 Francesca Collet , Richard C. Kraaij

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…

Probability · Mathematics 2025-12-08 Timothy M. Garoni , Aram Perez , Zongzheng Zhou

We derive Cram\'{e}r type moderate deviations for stationary sequences of bounded random variables. Our results imply the moderate deviation principles and a Berry-Esseen bound. Applications to quantile coupling inequalities, functions of…

Probability · Mathematics 2019-07-04 Xiequan Fan

The Curie-Weiss model is an exactly soluble model of ferromagnetism that allows one to study in detail the thermodynamic functions, in particular their properties in the neighbourhood of the critical temperature. In this model every…

Statistical Mechanics · Physics 2021-10-15 Martin Kochmański , Tadeusz Paszkiewicz , Sławomir Wolski

We use a new method via $p$-Wasserstein bounds to prove Cram\'er-type moderate deviations in (multivariate) normal approximations. In the classical setting that $W$ is a standardized sum of $n$ independent and identically distributed…

Probability · Mathematics 2022-05-27 Xiao Fang , Yuta Koike

In this article we consider an extension of the classical Curie-Weiss model in which the global and deterministic external magnetic field is replaced by local and random external fields which interact with each spin of the system. We prove…

Probability · Mathematics 2013-04-18 Matthias Löwe , Raphael Meiners , Felipe Torres

We modify the Glauber dynamics of the Curie-Weiss model with dissipation in Dai Pra, Fischer, Regoli[2013] by considering arbitrary transition rates and we analyze the phase-portrait as well as the dynamics of moderate fluctuations for…

Probability · Mathematics 2020-05-27 Francesca Collet , Richard C. Kraaij

We consider the dilute Curie-Weiss model of size $N$, which is a generalization of the classical Curie-Weiss model where the dependency structure between the spins is not encoded by the complete graph but via the (directed)…

Probability · Mathematics 2026-03-11 Fabian Apostel , Hanna Döring , Kristina Schubert
‹ Prev 1 2 3 10 Next ›