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Using an Eulerian perturbative calculation, we show that the distribution of relative pairwise velocities which arises from gravitational instability of Gaussian density fluctuations has asymmetric (skewed) exponential tails. The negative…

Astrophysics · Physics 2009-10-30 Roman Juszkiewicz , Karl B. Fisher , Istvan Szapudi

We compute the skewness of the matter distribution arising from non-linear evolution and from non-Gaussian initial perturbations. We apply our result to a very generic class of models with non-Gaussian initial conditions and we estimate…

Astrophysics · Physics 2009-12-30 Ruth Durrer , Roman Juszkiewicz , Martin Kunz , Jean-Philippe Uzan

In this paper we propose a framework that enables the study of large deviations for point processes based on stationary sequences with regularly varying tails. This framework allows us to keep track not of the magnitude of the extreme…

Probability · Mathematics 2009-08-21 Henrik Hult , Gennady Samorodnitsky

State-space models are pivotal for dynamic system analysis but often struggle with outlier data that deviates from Gaussian distributions, frequently exhibiting skewness and heavy tails. This paper introduces a robust extension utilizing…

Signal Processing · Electrical Eng. & Systems 2025-07-31 Yifan Yu , Shengjie Xiu , Daniel P. Palomar

Diffusion with stochastic transport is investigated here when the random driving process is a very general Gaussian process, including Fractional Brownian motion. The purpose is the comparison with a deterministic PDE, which in certain…

Probability · Mathematics 2026-04-20 Franco Flandoli , Francesco Russo

For a large $n\times m$ Gaussian matrix, we compute the joint statistics, including large deviation tails, of generalized and total variance - the scaled log-determinant $H$ and trace $T$ of the corresponding $n\times n$ covariance matrix.…

Statistical Mechanics · Physics 2016-04-29 Fabio Deelan Cunden , Pierpaolo Vivo

While time-delay lenses can be an independent probe of $H_0$ the estimates are degenerate with the convergence of the lens near the Einstein radius. Velocity dispersions, $\sigma$, can be used to break the degeneracy, with uncertainties…

Astrophysics of Galaxies · Physics 2026-02-05 R. Forés-Toribio , C. S. Kochanek , J. A. Muñoz

The aviation industry is of great importance for a globally connected economy. Customer satisfaction with airlines and airport performance is considerably influenced by how much flights are delayed. But how should the delay be quantified…

Physics and Society · Physics 2021-04-01 Evangelos Mitsokapas , Benjamin Schäfer , Rosemary J. Harris , Christian Beck

We consider the rate-distortion function for lossy source compression, as well as the channel capacity for error correction, through the lens of distributional robustness. We assume that the distribution of the source or of the additive…

Information Theory · Computer Science 2024-05-14 Vikrant Malik , Taylan Kargin , Victoria Kostina , Babak Hassibi

Primordial, non-Gaussian perturbations can generate scale-dependent bias in the galaxy distribution. This in turn will modify correlations between galaxy positions and peculiar velocities at late times, since peculiar velocities reflect the…

Cosmology and Nongalactic Astrophysics · Physics 2015-06-16 Yin-Zhe Ma , James E. Taylor , Douglas Scott

The results of a series of theoretical studies are reported, examining the convergence rate for different approximate representations of $\alpha$-stable distributions. Although they play a key role in modelling random processes with jumps…

Probability · Mathematics 2020-01-03 Marina Riabiz , Tohid Ardeshiri , Ioannis Kontoyiannis , Simon Godsill

In some fields of applications of stable distributions, especially in economics, it appears, that data have distributions similar to stable in a large region, but do not have such heavy tails. Our aim in this note is to propose several…

Probability · Mathematics 2014-03-17 Lenka Slámová , Lev B. Klebanov

Process Monitoring involves tracking a system's behaviors, evaluating the current state of the system, and discovering interesting events that require immediate actions. In this paper, we consider monitoring temporal system state sequences…

Machine Learning · Statistics 2018-07-11 Yihuang Kang , Vladimir Zadorozhny

This paper introduces the use of statistical distributions based on transport differential equations for clear distinction of transport modes within transient kinetic experiments. More specifically,novel techniques are developed for the…

Applications · Statistics 2025-01-08 M. Ross Kunz , Debtanu Maiti , Gregory Yablonsky , Rebecca Fushimi

We consider the optimal transport problem between multivariate Gaussian stationary stochastic processes. The transportation effort is the variance of the filtered discrepancy process. The main contribution of this technical note is to show…

Optimization and Control · Mathematics 2021-01-12 Mattia Zorzi

We introduce the Gaussian transform (GT), an optimal transport inspired iterative method for denoising and enhancing latent structures in datasets. Under the hood, GT generates a new distance function (GT distance) on a given dataset by…

Machine Learning · Computer Science 2020-06-23 Kun Jin , Facundo Mémoli , Zhengchao Wan

The q-Gaussians are a class of stable distributions which are present in many scientific fields, and that behave as heavy tailed distributions for an especific range of q values. The identification of these values, which are used in the…

Data Analysis, Statistics and Probability · Physics 2015-06-11 E. L de Santa Helena , C. M. Nascimento , G. J. L. Gerhardt

We study numerically the distributions of the length $L$ of the longest increasing subsequence (LIS) for the two cases of random permutations and of one-dimensional random walks. Using sophisticated large-deviation algorithms, we are able…

Disordered Systems and Neural Networks · Physics 2019-04-05 Jörn Börjes , Hendrik Schawe , Alexander K. Hartmann

This paper introduces a novel Bayesian approach to detect changes in the variance of a Gaussian sequence model, focusing on quantifying the uncertainty in the change point locations and providing a scalable algorithm for inference. Such a…

Methodology · Statistics 2025-03-04 Lorenzo Cappello , Oscar Hernan Madrid Padilla

The presence of non-Gaussian tails is a prevalent characteristic in many financial modeling scenarios, necessitating the use of complex non-Gaussian distributions such as the generalized beta of the second kind (GB2) and the skewed…

Applications · Statistics 2025-12-10 Xing Yan , Yue Zhao , Qi Wu , Wenxuan Ma