Related papers: When Independent Gaussian Models Break Down: Chara…
We study the one component $\Phi^4$ model for four different lattice actions in the Gaussian limit and for the Ising model in the broken phase. Emphasis is put on the euclidean invariance properties of the boson propagator. A measure of the…
Conditional independence in a multivariate normal (or Gaussian) distribution is characterized by the vanishing of subdeterminants of the distribution's covariance matrix. Gaussian conditional independence models thus correspond to algebraic…
We consider possible scale-dependence of the non-linearity parameter f_NL in local and quasi-local models of non-Gaussian primordial density perturbations. In the simplest model where the primordial perturbations are a quadratic local…
The Gaussian-time-dependent variational equations are used to explored the physics of $(\phi^4)_{3+1}$ field theory. We have investigated the static solutions and discussed the conditions of renormalization. Using these results and…
Inferring dependence structure through undirected graphs is crucial for uncovering the major modes of multivariate interaction among high-dimensional genomic markers that are potentially associated with cancer. Traditionally, conditional…
Gaussian mixture models are widely used to model data generated from multiple latent sources. Despite its popularity, most theoretical research assumes that the labels are either independent and identically distributed, or follows a Markov…
In strongly-coupled theories with no small parameters, there are factors of 4\pi that appear when the couplings of the low-energy effective lagrangian are written in units of the effective cutoff \Lambda. These numerical factors can be…
In the paper a self-consistent theoretical description of the lattice and magnetic properties of a model system with magnetoelastic interaction is presented. The dependence of magnetic exchange integrals on the distance between interacting…
We discuss models where N=1 global supersymmetry is spontaneously broken, at the classical level, in the presence of non-anomalous gauge interactions. We take such models as effective theories, valid up to some suitable scale and arising…
We prove that any scaling limit of a critical reflection positive Ising or $\varphi^4$ model of effective dimension $d_{\text{eff}}$ at least four is Gaussian. This extends the recent breakthrough work of Aizenman and Duminil-Copin -- which…
The spontaneous symmetry breaking at zero temperature in the four-component four-dimensional scalar $\lambda \phi^4_4$ model (the O(4) model) is investigated on a lattice for different values of the coupling constant $\lambda$. A general…
While supersymmetric extensions of the Standard Model can be fully described in terms of explicitly broken global supersymmetry, this description is only effective. Once related to spontaneous breaking in a more fundamental theory, the…
We prove that the scaling limits of spin fluctuations in four-dimensional Ising-type models with nearest-neighbor ferromagnetic interaction at or near the critical point are Gaussian. A similar statement is proven for the $\lambda \phi^4$…
Systems of interacting fermions can give rise to ground states whose correlations become effectively free-fermion-like in the thermodynamic limit, as shown by Baxter for a class of integrable models that include the one-dimensional XYZ…
We consider a model for multivariate data with heavy-tailed marginal distributions and a Gaussian dependence structure. The different marginals in the model are allowed to have non-identical tail behavior in contrast to most popular…
We consider the role that gauge symmetry breaking terms play on the continuum limit of gauge theories in three dimensions. As a paradigmatic example we consider scalar electrodynamics in which $N_f$ complex scalar fields interact with a…
Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…
Graphical models provide a framework for exploration of multivariate dependence patterns. The connection between graph and statistical model is made by identifying the vertices of the graph with the observed variables and translating the…
We introduce a sufficient graphical model by applying the recently developed nonlinear sufficient dimension reduction techniques to the evaluation of conditional independence. The graphical model is nonparametric in nature, as it does not…
We examine the unitarity properties of spontaneously broken non-commutative gauge theories. We find that the symmetry breaking mechanism in the non-commutative Standard Model of Chaichian et al. leads to an unavoidable violation of…