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A model for the diffusion of vector fields driven by external forces is proposed. Using the renormalization group and the $\epsilon$-expansion, the dynamical critical properties of the model with gaussian noise for dimensions below the…
We prove and discuss three results on zero distribution of gaussian analytic functions: (i) the Edeleman-Kostlan formula for the expectation of the counting measure; (ii) a variation on the theme of Calabi's rigidity theorem; (iii) Offord's…
We obtain in closed form the probability distribution for individual measurements of the stress-energy tensor of two-dimensional conformal field theory in the vacuum state, smeared in time against a Gaussian test function. The result is a…
Eigenvalue distributions are important dynamical quantities in matrix models, and it is a challenging problem to derive them in tensor models. In this paper, we consider real symmetric order-three tensors with Gaussian distributions as the…
The addition or subtraction of a photon from a Gaussian state of light is a versatile and experimentally feasible procedure to create non-Gaussian states. In multimode setups, these states manifest a wide range of phenomena when the photon…
Overlap fermions, which preserve exact chiral symmetry on the lattice, provide a powerful tool for investigating the topological structure of the vacuum. Applying this formulation to zero-temperature quenched SU(3) configurations generated…
In this paper, we construct an intermediate distribution linking the Gaussian and the Cauchy distribution. We provide the probability density function and the corresponding characteristic function of the intermediate distribution. Because…
Geometrical objects describing the material geometry of continuously defective graphene sheets are introduced and their compatibility conditions are formulated. Effective edge dislocations embedded in the Riemann-Cartan material space and…
Two types of Gaussian processes, namely the Gaussian field with generalized Cauchy covariance (GFGCC) and the Gaussian sheet with generalized Cauchy covariance (GSGCC) are considered. Some of the basic properties and the asymptotic…
The algorithm to calculate the generating function for the number of ``skeleton'' diagrams for the irreducible self-energy and vertex parts is derived for the problems with Gaussian random fields. We find an exact recurrence relation…
We consider a two-dimensional Coulomb gas of positive and negative pointlike unit charges interacting via a logarithmic potential. The density (rather than the charge) correlation functions are studied. In the bulk, the form-factor theory…
We show that if an interlacing particle system in a two-dimensional lattice is a determinantal point process, and the correlation kernel can be expressed as a double integral with certain technical assumptions, then the moments of the…
We study the asymptotic zero distribution of type II multiple orthogonal polynomials associated with two Macdonald functions (modified Bessel functions of the second kind). Based on the four-term recurrence relation, it is shown that, after…
We study a class of phase-space distribution functions that is generated from a Gaussian convolution of the Wigner distribution function. This class of functions represents the joint count probability in simultaneous measurements of…
The Gaussian curvature of a two-dimensional Riemannian manifold is uniquely determined by the choice of the metric. The formulas for computing the curvature in terms of components of the metric, in isothermal coordinates, involve the…
A new method to visualize the curvature of spacetime was recently proposed. This method finds the eigenvectors of the "electric" and "magnetic" components of the Weyl tensor and, in analogy to the field lines of electromagnetism, uses the…
Diffusion tensor coefficients play a central role in describing cosmic-ray transport in various astrophysical environments permeated with magnetic fields, which are usually modeled as a fluctuating field on top of a mean field. In this…
In this paper we study sectional curvature bounds for Riemannian manifolds with density from the perspective of a weighted torsion free connection introduced recently by the last two authors. We develop two new tools for studying weighted…
We provide a general formula for calculating correlators of arbitrary function of a Gaussian field. This work extends the standard leading-order approximation based on the delta N formalism to the case where truncation of the delta N at…
Derivation of two-time second-order correlation function by following approaches such as stochastic differential equation, coherent-state propagator, and quasi-statistical distribution function is presented. In the process, the time…