Related papers: When Independent Gaussian Models Break Down: Chara…
Two approaches to incorporate heterogeneity in discrete models are compared. In the first, standard approach, the heterogeneity is dictated by geometrical structure of the discrete system. In the second approach, the heterogeneity is…
Functional graphical models have undergone extensive development during the recent years, leading to a variety models such as the functional Gaussian graphical model, the functional copula Gaussian graphical model, the functional Bayesian…
Gaussian bounds on noise correlation of functions play an important role in hardness of approximation, in quantitative social choice theory and in testing. The author (2008) obtained sharp gaussian bounds for the expected correlation of…
Learning dependence relationships among variables of mixed types provides insights in a variety of scientific settings and is a well-studied problem in statistics. Existing methods, however, typically rely on copious, high quality data to…
We consider the large-N $\Phi^4$ theory with spontaneously broken symmetry at finite temperature. We study, in the large-N limit, quantum states which are characterized by a time dependent, spatially homogenous expectation value of one of…
The concept of (global) gauge symmetry breaking plays an important role in many areas of physics. Since the corresponding symmetry is a gauge symmetry, its breaking is actually gauge-dependent. Thus, it is possible to design gauges which…
The simulation of real-time dynamics in lattice gauge theories is particularly hard for classical computing due to the exponential scaling of the required resources. On the other hand, quantum algorithms can potentially perform the same…
We discuss a class of discrete Gaussian free fields on Hamming graphs, where interactions are determined solely by the Hamming distance between vertices. The purpose of examining this class is that it differs significantly from the commonly…
Graphical models have long been studied in statistics as a tool for inferring conditional independence relationships among a large set of random variables. The most existing works in graphical modeling focus on the cases that the data are…
We discuss models of primordial density perturbations where the non-Gaussianity is strongly scale-dependent. In particular, the non-Gaussianity may have a sharp cut-off and be very suppressed on large cosmological scales, but sizeable on…
The accuracy of probability distributions inferred using machine-learning algorithms heavily depends on data availability and quality. In practical applications it is therefore fundamental to investigate the robustness of a statistical…
Consider jointly Gaussian random variables whose conditional independence structure is specified by a graphical model. If we observe realizations of the variables, we can compute the covariance matrix, and it is well known that the support…
In models with dynamical electroweak symmetry breaking, this breaking is normally communicated to quarks and leptons by a set of vector bosons with masses generated via sequential breaking of a larger gauge symmetry. In reasonably…
This paper presents a framework for modeling failure in quasi-brittle geomaterials under different loading conditions. A micromechanics-based model is proposed in which the field variables are linked to physical mechanisms at the microcrack…
Using molecular dynamics simulations of an incommensurate Au(111)/graphite interface, we investigate the conditions under which structural lubricity produces load-independent friction. We show that strict load independence occurs only in…
We consider the approximations behind the typical mean-field model derived for a class of systems made up of type II excitable units influenced by noise and coupling delays. The formulation of the two approximations, referred to as the…
We study the large-$N$ scaling behavior of the $\theta$ dependence of the ground-state energy density $E(\theta)$ of four-dimensional (4D) $SU(N)$ gauge theories and two-dimensional (2D) $CP^{N-1}$ models, where $\theta$ is the parameter…
We introduce a variational ansatz based on Gaussian states for (1+1)-dimensional lattice gauge models. To this end we identify a set of unitary transformations which decouple the gauge degrees of freedom from the matter fields. Using our…
Note: Accepted version, published in Statistical Papers, https://doi.org/10.1007/s00362-023-01414-3. It is shown that some theoretically identifiable parameters cannot be empirically identified, meaning that no consistent estimator of them…
We describe various sets of conditional independence relationships, sufficient for qualitatively comparing non-vanishing squared partial correlations of a Gaussian random vector. These sufficient conditions are satisfied by several…