English
Related papers

Related papers: Extremes of some Gaussian random interfaces

200 papers

We present a practical way of introducing convolutional structure into Gaussian processes, making them more suited to high-dimensional inputs like images. The main contribution of our work is the construction of an inter-domain inducing…

Machine Learning · Statistics 2017-09-07 Mark van der Wilk , Carl Edward Rasmussen , James Hensman

We consider upper level-sets of the Gaussian free field on $\mathbb Z^d$, for $d\geq 3$, above a given real-valued height parameter $h$. As $h$ varies, this defines a canonical percolation model with strong, algebraically decaying…

Probability · Mathematics 2024-06-26 Hugo Duminil-Copin , Subhajit Goswami , Pierre-François Rodriguez , Franco Severo

We study gradient models on the lattice $\mathbb{Z}^d$ with non-convex interactions. These Gibbs fields (lattice models with continuous spin) emerge in various branches of physics and mathematics. In quantum field theory they appear as…

Mathematical Physics · Physics 2016-08-06 Stefan Adams , Roman Kotecký , Stefan Müller

A new unimodal distribution family indexed by the mode and three other parameters is derived from a mixture of a Gumbel distribution for the maximum and a Gumbel distribution for the minimum. Properties of the proposed distribution are…

Methodology · Statistics 2024-07-02 Qingyang Liu , Xianzheng Huang , Haiming Zhou

The article addresses a long-standing open problem on the justification of using variational Bayes methods for parameter estimation. We provide general conditions for obtaining optimal risk bounds for point estimates acquired from…

Statistics Theory · Mathematics 2017-12-27 Debdeep Pati , Anirban Bhattacharya , Yun Yang

A sequence of accompanying laws is suggested in the limit theorem of B. V. Gnedenko for maximums of independent random variables belonging to maximum domain of attraction of the Gumbel distribution. It is shown that this sequence gives an…

Probability · Mathematics 2020-10-22 V. I. Piterbarg , Yu. A. Scherbakova

In this paper we display a direct and physically attractive derivation of the screening contribution to the interaction potential in the Chiral Schwinger model and generalized Maxwell-Chern-Simons gauge theory. It is shown that these…

High Energy Physics - Theory · Physics 2009-11-07 Patricio Gaete , Iván Schmidt

We propose a determinant-free approach for simulation-based Bayesian inference in high-dimensional Gaussian models. We introduce auxiliary variables with covariance equal to the inverse covariance of the model. The joint probability of the…

Computation · Statistics 2017-09-12 Louis Ellam , Heiko Strathmann , Mark Girolami , Iain Murray

We present numerical studies of wetting on various topographic substrates, including random topographies. We find good agreement with recent predictions based on an analytical interface-displacement-type theory \cite{Herminghaus2012,…

Fluid Dynamics · Physics 2016-03-23 Renaud Dufour , Ciro Semprebon , Stephan Herminghaus

We study the tail behavior of the distribution of the sum of asymptotically independent risks whose marginal distributions belong to the maximal domain of attraction of the Gumbel distribution. We impose conditions on the distribution of…

Probability · Mathematics 2009-06-29 Abhimanyu Mitra , Sidney I. Resnick

This is the first in a series of two works which study the discrete Gaussian free field on the binary tree when all leaves are conditioned to be positive. In this work, we obtain sharp asymptotics for the probability of this "hard-wall…

Probability · Mathematics 2024-09-04 Maximilian Fels , Lisa Hartung , Oren Louidor

We prove that the phase transition for the Gaussian free field (GFF) is sharp. In comparison to a previous argument due to Rodriguez in 2017 which characterized a $0-1$ law for the Massive Gaussian Free Field by analyzing crossing…

Probability · Mathematics 2024-08-08 Pete Rigas

In this paper, we derive tail approximations of integrals of exponential functions of Gaussian random fields with varying mean functions and approximations of the associated point processes. This study is motivated naturally by multiple…

Statistics Theory · Mathematics 2011-12-05 Jingchen Liu , Gongjun Xu

This paper is devoted to the Gaussian fluctuations and deviations of the traces of tridiagonal random matrix. Under quite general assumptions, we prove that the traces are approximately normal distributed. Multi-dimensional central limit…

Probability · Mathematics 2015-06-16 Deng Zhang

We consider in this paper the collection of near maxima of the discrete, two dimensional Gaussian free field in a box with Dirichlet boundary conditions. We provide a rough description of the geometry of the set of near maxima, estimates on…

Probability · Mathematics 2013-04-09 Jian Ding , Ofer Zeitouni

Completing the study initiated by Mounaix and Collet [J. Stat. Phys. {\bf 143}, 139-147 (2011)], we investigate the realizations of a Gaussian random field in the limit where a given (general) quadratic form of the field is large.…

Mathematical Physics · Physics 2015-09-15 Philippe Mounaix

Regularly varying stochastic processes are able to model extremal dependence between process values at locations in random fields. We investigate the empirical extremogram as an estimator of dependence in the extremes. We provide conditions…

Statistics Theory · Mathematics 2017-04-11 Sven Buhl , Claudia Klüppelberg

We study the convergence properties of the Gibbs Sampler in the context of posterior distributions arising from Bayesian analysis of conditionally Gaussian hierarchical models. We develop a multigrid approach to derive analytic expressions…

Computation · Statistics 2019-06-27 Giacomo Zanella , Gareth Roberts

We derive the limiting distributions of exceedances point processes of randomly scaled weakly dependent stationary Gaussian sequences under some mild asymptotic conditions. In the literature analogous results are available only for…

Probability · Mathematics 2013-10-22 Enkelejd Hashorva , Zuoxiang Peng , Zhichao Weng

We use Stein's method to obtain bounds on the rate of convergence for a class of statistics in geometric probability obtained as a sum of contributions from Poisson points which are exponentially stabilizing, i.e. locally determined in a…

Probability · Mathematics 2007-05-23 Mathew D. Penrose , J. E. Yukich