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We develop large sample theory for merged data from multiple sources. Main statistical issues treated in this paper are (1) the same unit potentially appears in multiple datasets from overlapping data sources, (2) duplicated items are not…
We delve into the in-in formalism and derive general expressions for the computation of n-point functions for a self-interacting scalar field by means of a probability density functional (PDF). Even though in typical situations these…
A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and L\'evy distributions are proposed and functional central limit theorems using the uniform…
In this paper we propose a new approach for sequential monitoring of a parameter of a $d$-dimensional time series, which can be estimated by approximately linear functionals of the empirical distribution function. We consider a…
We present a new approach to study measures on ensembles of contours, polymers or other objects interacting by some sort of exclusion condition. For concreteness we develop it here for the case of Peierls contours. Unlike existing methods,…
We introduce the coverage correlation coefficient, a novel nonparametric measure of statistical association designed to quantifies the extent to which two random variables have a joint distribution concentrated on a singular subset with…
Elkies and McMullen [Duke Math.J.~123 (2004) 95--139] have shown that the gaps between the fractional parts of \sqrt n for n=1,\ldots,N, have a limit distribution as N tends to infinity. The limit distribution is non-standard and differs…
We study a one-dimensional anisotropic exclusion process describing particles injected at the origin, moving to the right on a chain of $L$ sites and being removed at the (right) boundary. We construct the steady state and compute the…
A number of recent studies have estimated the inter-galactic void probability function and investigated its departure from various random models. We study a family of parametric statistical models based on gamma distributions, which do give…
In Bayesian nonparametric inference, random discrete probability measures are commonly used as priors within hierarchical mixture models for density estimation and for inference on the clustering of the data. Recently, it has been shown…
We developed a modification to the calculation of the two-point correlation function commonly used in the analysis of large scale structure in cosmology. An estimator of the two-point correlation function is constructed by contrasting the…
The notion of probability density for a random function is not as straightforward as in finite-dimensional cases. While a probability density function generally does not exist for functional data, we show that it is possible to develop the…
We study elastic systems such as interfaces or lattices, pinned by quenched disorder. To escape triviality as a result of ``dimensional reduction'', we use the functional renormalization group. Difficulties arise in the calculation of the…
The second part of the paper mainly deals with convergence of infinite determinantal measures, understood as the convergence of the approximating finite determinantal measures. In addition to the usual weak topology on the space of…
This article develops an analytical framework for studying information divergences and likelihood ratios associated with Poisson processes and point patterns on general measurable spaces. The main results include explicit analytical…
We study various temporal correlation functions of a tagged particle in one-dimensional systems of interacting point particles evolving with Hamiltonian dynamics. Initial conditions of the particles are chosen from the canonical thermal…
Two and three point functions of composite operators are analysed with regard to (logarithmically) divergent contact terms. Using the renormalisation group of dimensional regularisation it is established that the divergences are governed by…
We propose a new powerful family of tests of univariate normality. These tests are based on an initial value problem in the space of characteristic functions originating from the fixed point property of the normal distribution in the zero…
We construct a family of probability measures on the group of Hamiltonian diffeomorphisms of a closed symplectic manifold $(M,\omega)$. We show that these measures are Borel measures with respect to the topology induced by the Hofer metric.…
We consider Markov chains on the space of (countable) partitions of the interval $[0,1]$, obtained first by size biased sampling twice (allowing repetitions) and then merging the parts with probability $\beta_m$ (if the sampled parts are…