Related papers: Cluster expansions for Gibbs point processes
We introduce a generic scheme to perform non-perturbative linked cluster expansions in long-range ordered quantum phases. Clusters are considered to be surrounded by an ordered reference state leading to effective edge-fields in the exact…
In this paper we present a novel iterative multiphase clustering technique for efficiently clustering high dimensional data points. For this purpose we implement clustering feature (CF) tree on a real data set and a Gaussian density…
The Kirkwood superposition is a well-known tool in statistical physics to approximate the $n$-point correlation functions for $n\geq 3$ in terms of the density $\rho $ and the radial distribution function $g$ of the underlying system.…
We study the convergence properties of the Gibbs Sampler in the context of posterior distributions arising from Bayesian analysis of conditionally Gaussian hierarchical models. We develop a multigrid approach to derive analytic expressions…
A general expansion scheme based on the concept of linked cluster expansion from the theory of classical spin systems is constructed for models of interacting electrons. It is shown that with a suitable variational formulation of mean-field…
We use a statistical model to discuss nonequilibrium fragmentation phenomena taking place in the stochastic dynamics of the log sector in log gravity. From the canonical Gibbs model, a combinatorial analysis reveals an important aspect of…
Many models for point process data are defined through a thinning procedure where locations of a base process (often Poisson) are either kept (observed) or discarded (thinned). In this paper, we go back to the fundamentals of the…
We present a Dirichlet process mixture model over discrete incomplete rankings and study two Gibbs sampling inference techniques for estimating posterior clusterings. The first approach uses a slice sampling subcomponent for estimating…
We propose a hypergraph expansion which facilitates the direct treatment of quantum spin models with many-site interactions via perturbative linked cluster expansions. The main idea is to generate all relevant subclusters and sort them into…
Widely used models in genetics include the Wright-Fisher diffusion and its moment dual, Kingman's coalescent. Each has a multilocus extension but under neither extension is the sampling distribution available in closed-form, and their…
We establish that the dispersion relations of any physical system composed of two coupled subsystems, governed by a space-time homogeneous Lagrangian, admit a factorized form G_{1}G_{2}=\gamma G_{\mathrm{c}}, where G_{1} and G_{2} are the…
We study how the two-point density correlation properties of a point particle distribution are modified when each particle is divided, by a stochastic process, into an equal number of identical "daughter" particles. We consider generically…
Recent advances in engineering technologies have enabled the collection of a large number of longitudinal features. This wealth of information presents unique opportunities for researchers to investigate the complex nature of diseases and…
We apply a new statistics, the factorial moment correlators, to density maps obtained from the APM survey. The resulting correlators are all proportional to the two point correlation function, substantially amplified, with an amplification…
Let $p_1 \ge p_2 \ge \dots$ be the prime factors of a random integer chosen uniformly from $1$ to $n$, and let $$ \frac{\log p_1}{\log n}, \frac{\log p_2}{\log n}, \dots $$ be the sequence of scaled log factors. Billingsley's Theorem…
Motivated by the fundamental problem of measuring species diversity, this paper introduces the concept of a cluster structure to define an exchangeable cluster probability function that governs the joint distribution of a random count and…
We establish sample-path large deviation principles for the centered cumulative functional of marked Poisson cluster processes in the Skorokhod space equipped with the M1 topology, under joint regular variation assumptions on the marks and…
We use Numerical Linked Cluster Expansions (NLCE) to study the site diluted transverse-field Ising model on the square-lattice at $T=0$. NLCE with a self-consistent mean-field on the boundary of the clusters is used to obtain the ground…
Recent years have seen the development of two types of non-local extensions to the single-site dynamical mean field theory. On one hand, cluster approximations, such as the dynamical cluster approximation, recover short-range…
We discuss the relationship between discrete-time processes (chains) and one-dimensional Gibbs measures. We consider finite-alphabet (finite-spin) systems, possibly with a grammar (exclusion rule). We establish conditions for a stochastic…