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We develop asymptotic theory for weighted likelihood estimators (WLE) under two-phase stratified sampling without replacement. We also consider several variants of WLEs involving estimated weights and calibration. A set of empirical process…

Statistics Theory · Mathematics 2013-04-09 Takumi Saegusa , Jon A. Wellner

We consider the six-vertex model with domain wall boundary conditions. We choose the inhomogeneities as solutions of the Bethe Ansatz equations. The Bethe Ansatz equations have many solutions, so we can consider a wide variety of…

Mathematical Physics · Physics 2009-11-07 J. de Gier , V. Korepin

Although it is well-known that some exponential family random graph model (ERGM) families exhibit phase transitions (in which small parameter changes lead to qualitative changes in graph structure), the behavior of other models is still…

Social and Information Networks · Computer Science 2020-01-07 Carter T. Butts

We study concentration properties of vertex degrees of $n$-dimensional Erdos-R\'enyi random graphs with the edge probability $\rho/n$ by means of high moments of these random variables in the limit when $n$ and $\rho$ tend to infinity.…

Probability · Mathematics 2020-07-23 O. Khorunzhiy

The unconstrained exponential family of random graphs assumes no prior knowledge of the graph before sampling, but it is natural to consider situations where partial information about the graph is known, for example the total number of…

Probability · Mathematics 2017-04-19 Richard Kenyon , Mei Yin

We study a class models of correlated random networks in which vertices are characterized by \textit{hidden variables} controlling the establishment of edges between pairs of vertices. We find analytical expressions for the main topological…

Disordered Systems and Neural Networks · Physics 2009-11-10 Marian Boguna , Romualdo Pastor-Satorras

Many environmental processes exhibit weakening spatial dependence as events become more extreme. Well-known limiting models, such as max-stable or generalized Pareto processes, cannot capture this, which can lead to a preference for models…

Methodology · Statistics 2017-09-06 Raphaël G. Huser , Jennifer L. Wadsworth

We obtain asymptotic formulas for the partition function of the six-vertex model with domain wall boundary conditions and half-turn symmetry in each of the phase regions. The proof is based on the Izergin--Korepin--Kuperberg determinantal…

Mathematical Physics · Physics 2017-11-06 Pavel Bleher , Karl Liechty

There is a rich literature proposing methods and establishing asymptotic properties of Bayesian variable selection methods for parametric models, with a particular focus on the normal linear regression model and an increasing emphasis on…

Statistics Theory · Mathematics 2011-08-16 Suprateek Kundu , David B. Dunson

We consider random graphs with a given degree sequence and show, under weak technical conditions, asymptotic normality of the number of components isomorphic to a given tree, first for the random multigraph given by the configuration model…

Probability · Mathematics 2019-02-01 Svante Janson

We prove asymptotic normality for the number of fringe subtrees isomorphic to any given tree in uniformly random trees with given vertex degrees. As applications, we also prove corresponding results for random labelled trees with given…

Probability · Mathematics 2023-12-08 Gabriel Berzunza Ojeda , Cecilia Holmgren , Svante Janson

We study the asymptotics for sparse exponential random graph models where the parameters may depend on the number of vertices of the graph. We obtain exact estimates for the mean and variance of the limiting probability distribution and the…

Probability · Mathematics 2017-04-19 Mei Yin , Lingjiong Zhu

This paper investigates the {\em nonasymptotic} properties of Bayes procedures for estimating an unknown distribution from $n$ i.i.d.\ observations. We assume that the prior is supported by a model $(\scr{S},h)$ (where $h$ denotes the…

Statistics Theory · Mathematics 2014-11-03 Lucien Birgé

We introduce a random intersection graph process aimed at modeling sparse evolving affiliation networks that admit tunable (power law) degree distribution and assortativity and clustering coefficients. We show the asymptotic degree…

Probability · Mathematics 2013-01-24 Mindaugas Bloznelis , Michal Karonski

We study the local asymptotics at the edge for particle systems arising from: (i) eigenvalues of sums of unitarily invariant random Hermitian matrices and (ii) signatures corresponding to decompositions of tensor products of representations…

Probability · Mathematics 2023-02-22 Andrew Ahn

In this paper, we investigate the asymptotic behavior of the Bergman kernel at the boundary for some pseudoconvex model domains. This behavior can be described by the geometrical information of the Newton polyhedron of the defining function…

Complex Variables · Mathematics 2023-08-17 Joe Kamimoto

We consider the asymptotic behaviour of the marginal maximum likelihood empirical Bayes posterior distribution in general setting. First we characterize the set where the maximum marginal likelihood estimator is located with high…

Statistics Theory · Mathematics 2016-04-05 Judith Rousseau , Botond Szabo

A random graph evolution rule is considered. The graph evolution is based on interactions of three vertices. The weight of a clique is the number of its interactions. The asymptotic behaviour of the weights is described. It is known that…

Probability · Mathematics 2014-12-23 István Fazekas , Csaba Noszály , Attila Perecsényi

We investigate the concept of an asymptotic e-process, which is a doubly-indexed stochastic process $(E_{m,n})_{m,n\in\mathbb{N}}$ that possesses, asymptotically for an approximation index $m\to\infty$, the properties of an e-process along…

Statistics Theory · Mathematics 2026-05-25 Pierre-François Massiani , Sebastian Schulze , Mattes Mollenhauer

We consider the preferential attachment model. This is a growing random graph such that at each step a new vertex is added and forms $m$ connections. The neighbors of the new vertex are chosen at random with probability proportional to…

Probability · Mathematics 2024-04-11 Simone Baldassarri , Gianmarco Bet