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We use Stein's method to establish the rates of normal approximation in terms of the total variation distance for a large class of sums of score functions of marked Poisson point processes on $\mathbb{R}^d$. As in the study under the weaker…

Probability · Mathematics 2020-11-17 Tianshu Cong , Aihua Xia

We approximate the distribution of the sum of independent but not necessarily identically distributed Bernoulli random variables using a shifted binomial distribution where the three parameters (the number of trials, the probability of…

Probability · Mathematics 2010-04-02 Vydas Čekanavičius , Erol A. Peköz , Adrian Röllin , Michael Shwartz

We prove a $pre$-$asymptotic$ bound on the total variation distance between the uniform distribution over two types of undirected graphs with $n$ nodes. One distribution places a prescribed number of $k_T$ triangles and $k_S$ edges not…

Probability · Mathematics 2015-09-30 Stephen DeSalvo , M. Puck Rombach

In this paper we develop a framework for multivariate functional approximation by a suitable Gaussian process via an exchangeable pairs coupling that satisfies a suitable approximate linear regression property, thereby building on work by…

Probability · Mathematics 2021-03-25 Christian Döbler , Mikołaj J. Kasprzak

Applying Stein's method, an inductive technique and size bias coupling yields a Berry-Esseen theorem for normal approximation without the usual restriction that the coupling be bounded. The theorem is applied to counting the number of…

Probability · Mathematics 2013-02-26 Larry Goldstein

It is generally known that counting statistics is not correctly described by a Gaussian approximation. Nevertheless, in neutron scattering, it is common practice to apply this approximation to the counting statistics; also at low counting…

Data Analysis, Statistics and Probability · Physics 2020-06-09 Jakob Lassa , Magnus Egede Bøggild , Per Hedegård , Kim Lefmann

We propose a new general version of Stein's method for univariate distributions. In particular we propose a canonical definition of the Stein operator of a probability distribution {which is based on a linear difference or differential-type…

Probability · Mathematics 2016-03-28 Christophe Ley , Gesine Reinert , Yvik Swan

Stein's method is used to prove limit theorems for random character ratios. Tools are developed for four types of structures: finite groups, Gelfand pairs, twisted Gelfand pairs, and association schemes. As one example an error term is…

Combinatorics · Mathematics 2007-05-23 Jason Fulman

Statistical field theory methods have been very successful with a number of random graph and random matrix problems, but it is challenging to apply these methods to graphs with prescribed degree sequences due to the extensive number of…

Statistical Mechanics · Physics 2025-05-20 Pawat Akara-pipattana , Oleg Evnin

We propose a simple algorithm generating labelled posets of given size according to the almost uniform distribution. By "almost uniform" we understand that the distribution of generated posets converges in total variation to the uniform…

Combinatorics · Mathematics 2018-10-15 Patryk Kozieł , Małgorzata Sulkowska

Quantification learning is the task of predicting the label distribution of a set of instances. We study this problem in the context of graph-structured data, where the instances are vertices. Previously, this problem has only been…

Machine Learning · Computer Science 2026-01-01 Clemens Damke , Eyke Hüllermeier

This paper extends the study of fringe trees in random plane trees with a given degree statistic. While previous work established the asymptotic normality of the count of fringe trees isomorphic to a fixed tree, we investigate the case…

Probability · Mathematics 2026-04-08 Gabriel Berzunza Ojeda , Cecilia Holmgren , Svante Janson

Sampling uniform simple graphs with power-law degree distributions with degree exponent $\tau\in(2,3)$ is a non-trivial problem. We propose a method to sample uniform simple graphs that uses a constrained version of the configuration model…

Probability · Mathematics 2017-11-17 Tom Bannink , Remco van der Hofstad , Clara Stegehuis

The derivation and application of Stein identities have received considerable research interest in recent years, especially for continuous or discrete-univariate distributions. In this paper, we complement the existing literature by…

Methodology · Statistics 2026-03-02 Shaochen Wang , Christian H. Weiß

We provide algorithms for the minimum 2-edge-connected spanning subgraph problem and the minimum 2-vertex-connected spanning subgraph problem with approximation ratio both $\frac{4}{3}$. Using a common theme, the algorithms and their…

Data Structures and Algorithms · Computer Science 2024-07-16 Ali Çivril

In this article, we consider Poisson and Poisson convoluted geometric approximation to the sums of $n$ independent random variables under moment conditions. We use Stein's method to derive the approximation results in total variation…

Probability · Mathematics 2020-07-07 Pratima Eknath Kadu

We study a new class of time inhomogeneous P\'olya-type urn schemes and give optimal rates of convergence for the distribution of the properly scaled number of balls of a given color to nearly the full class of generalized gamma…

Probability · Mathematics 2016-06-28 Erol A. Peköz , Adrian Röllin , Nathan Ross

Let $L$ be subset of $\{3,4,\dots\}$ and let $X_{n,M}^{(L)}$ be the number of cycles belonging to unicyclic components whose length is in $L$ in the random graph $G(n,M)$. We find the limiting distribution of $X_{n,M}^{(L)}$ in the…

Combinatorics · Mathematics 2020-12-29 Marc Noy , Vonjy Rasendrahasina , Vlady Ravelomanana , Juanjo Rué

We provide a general result for bounding the difference between point probabilities of integer supported distributions and the translated Poisson distribution, a convenient alternative to the discretized normal. We illustrate our theorem in…

Probability · Mathematics 2017-12-05 A. D. Barbour , Adrian Röllin , Nathan Ross

Preferential attachment graphs are random graphs designed to mimic properties of typical real world networks. They are constructed by a random process that iteratively adds vertices and attaches them preferentially to vertices that already…

Discrete Mathematics · Computer Science 2018-03-30 Jan Dreier , Philipp Kuinke , Peter Rossmanith