Related papers: Random sparse sampling in a Gibbs weighted tree
A new type of elasticity of random (multifractal) structures is suggested. A closed system of constitutive equations is obtained on the basis of two proposed phenomenological laws of reversible deformations of multifractal structures. The…
This study investigates the natural or intrinsic measure of a symbolic dynamical system $\Sigma$. The measure $\mu([i_{1},i_{2},...,i_{n}])$ of a pattern $[i_{1},i_{2},...,i_{n}]$ in $\Sigma$ is an asymptotic ratio of…
Consider a Markov chain on an infinite tree T=(V,E) rooted at \rho. In such a chain, once the initial root state \sigma(\rho) is chosen, each vertex iteratively chooses its state from the one of its parent by an application of a Markov…
This note deals with a problem of the probabilistic Ramsey theory in functional analysis. Given a linear operator $T$ on a Hilbert space with an orthogonal basis, we define the isomorphic structure $\Sigma(T)$ as the family of all subsets…
We study the multifractal analysis of self-similar measures arising from random homogeneous iterated function systems. Under the assumption of the uniform strong separation condition, we see that this analysis parallels that of the…
We use Dirichlet form methods to construct and analyze a reversible Markov process, the stationary distribution of which is the Brownian continuum random tree. This process is inspired by the subtree prune and regraft (SPR) Markov chains…
We introduce a new ensemble of random bipartite graphs, which we term the `smearing ensemble', where each left node is connected to some number of consecutive right nodes. Such graphs arise naturally in the recovery of sparse wavelet…
We study properties of a sample covariance estimate $\widehat \Sigma$ given a finite sample of $n$ i.i.d. centered random elements in $\R^d$ with the covariance matrix $\Sigma$. We derive dimension-free bounds on the squared Frobenius norm…
This paper studies large sample properties of a Bayesian approach to inference about slope parameters $\gamma$ in linear regression models with a structural break. In contrast to the conventional approach to inference about $\gamma$ that…
In this paper we define distance expanding random dynamical systems. We develop the appropriate thermodynamic formalism of such systems. We obtain in particular the existence and uniqueness of invariant Gibbs states, the appropriate…
We study "random surfaces," which are random real (or integer) valued functions on Z^d. The laws are determined by convex, nearest neighbor, difference potentials that are invariant under translation by a full-rank sublattice L of Z^d; they…
Weighted likelihood, in which one solves Horvitz-Thompson or inverse probability weighted (IPW) versions of the likelihood equations, offers a simple and robust method for fitting models to two phase stratified samples. We consider…
This paper proposes a geometric estimator of dependency between a pair of multivariate samples. The proposed estimator of dependency is based on a randomly permuted geometric graph (the minimal spanning tree) over the two multivariate…
A theoretical scaling law for the size effect of the strength of brittle materials is presented. To some extend, it can be seen as an extension of the well known Weibull law. For that a correlated Random Fields is used to model the…
Binary measurements arise naturally in a variety of statistical and engineering applications. They may be inherent to the problem---e.g., in determining the relationship between genetics and the presence or absence of a disease---or they…
Feature subsampling is a core component of random forests and other ensemble methods. While recent theory suggests that this randomization acts solely as a variance reduction mechanism analogous to ridge regularization, these results…
An empirical Bayes approach to the estimation of possibly sparse sequences observed in Gaussian white noise is set out and investigated. The prior considered is a mixture of an atom of probability at zero and a heavy-tailed density \gamma,…
The paper concerns lattice triangulations, that is, triangulations of the integer points in a polygon in $\mathbb{R}^2$ whose vertices are also integer points. Lattice triangulations have been studied extensively both as geometric objects…
The finite parts of a large, locally interacting many-body system prepared out-of-equilibrium eventually equilibrate. Characterising the underlying mechanisms of this process and its timescales, however, is particularly hard as it requires…
We investigate optically reconfigurable dielectric metamaterials at gigahertz frequencies. More precisely, we study the microwave response of a subwavelength grating optically imprinted into a semiconductor slab. In the homogenized regime,…