相关论文: Normal approximation for hierarchical structures

The Central Limit Theorem states that, in the limit of a large number of terms, an appropriately scaled sum of independent random variables yields another random variable whose probability distribution tends to a stable distribution. The…

I propose a new version of the Hierarchical Reference Theory of liquids. Two formalisms, one in the grand canonical ensemble, the other in the framework of statistical field theory are given in parallel. In the latter the theory is an…

We develop a variant of Stein's method of comparison of generators to bound the Kolmogorov, total variation, and Wasserstein-1 distances between distributions on the real line. Our discrepancy is expressed in terms of the ratio of reverse…

A consequence of de Finetti's representation theorem is that for every infinite sequence of exchangeable 0-1 random variables $(X_k)_{k\geq1}$, there exists a probability measure $\mu$ on the Borel sets of $[0,1]$ such that $\bar X_n =…

Modeling real-world distributions can often be challenging due to sample data that are subjected to perturbations, e.g., instrumentation errors, or added random noise. Since flow models are typically nonlinear algorithms, they amplify these…

Let M be a bounded domain of a Euclidian space with smooth boundary. We relate the Cheeger constant of M and the conductance of a neighborhood graph defined on a random sample from M. By restricting the minimization defining the latter over…

Let $ (Z_{n})_{n\geq 0} $ be a supercritical branching process in an independent and identically distributed random environment. We establish an optimal convergence rate in the Wasserstein-$1$ distance for the process $ (Z_{n})_{n\geq 0} $,…

A graph homomorphism between two graphs is a map from the vertex set of one graph to the vertex set of the other graph, that maps edges to edges. In this note we study the range of a uniformly chosen homomorphism from a graph G to the…

This paper introduces a general class of hierarchical nonparametric prior distributions. The random probability measures are constructed by a hierarchy of generalized species sampling processes with possibly non-diffuse base measures. The…

We discuss the classical problem of measuring the regularity of distribution of sets of $N$ points in $\mathbb{T}^d$. A recent line of investigation is to study the cost ($=$ mass $\times$ distance) necessary to move Dirac measures placed…

Consider a graph on randomly scattered points in an arbitrary space, with two points $x,y$ connected with probability $\phi(x,y)$. Suppose the number of points is large but the mean number of isolated points is $O(1)$. We give general…

We study crystal dynamics in the harmonic approximation. The atomic masses are weakly disordered, in the sense that their deviation from uniformity is of order epsilon^(1/2). The dispersion relation is assumed to be a Morse function and to…

Most graph kernels are an instance of the class of $\mathcal{R}$-Convolution kernels, which measure the similarity of objects by comparing their substructures. Despite their empirical success, most graph kernels use a naive aggregation of…

Given a sequence of $n$ identically distributed random variables with common distribution $F$, the \emph{fragility distribution of order $m$}, represented by $\FD$, is the limit conditional distribution of the number of exceedances given…

Define a random variable $\xi_n$ by choosing a conjugacy class $C$ of the Sylow $p$-subgroup of $S_{p^n}$ by random, and let $\xi_n$ be the logarithm of the order of an element in $C$. We show that $\xi_n$ has bounded variance and mean…

The characteristic sequence of hypergraphs $<P_n : n<\omega>$ associated to a formula $\phi(x;y)$, introduced in [arXiv:0908.4111], is defined by $P_n(y_1,... y_n) = (\exists x) \bigwedge_{i\leq n} \phi(x;y_i)$. This paper continues the…

We consider a class of growing random graphs obtained by creating vertices sequentially one by one: at each step, we choose uniformly the neighbours of the newly created vertex; its degree is a random variable with a fixed but arbitrary…

In this paper we propose tight upper and lower bounds for the Wasserstein distance between any two {{univariate continuous distributions}} with probability densities $p_1$ and $p_2$ having nested supports. These explicit bounds are…

Finding the mean of sampled data is a fundamental task in machine learning and statistics. However, in cases where the data samples are graph objects, defining a mean is an inherently difficult task. We propose a novel framework for…

Motivated by the omnipresence of extreme value distributions in limit theorems involving extremes of random processes, we adapt Stein's method to include these laws as possible target distributions. We do so by using the generator approach…