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Matrix-valued covariance functions are crucial to geostatistical modeling of multivariate spatial data. The classical assumption of symmetry of a multivariate covariance function is overlay restrictive and has been considered as unrealistic…
In a Quantum Field Theory with a time-dependent background, time-translational symmetry is broken. We therefore expect time-dependent loop corrections to cosmological observables after renormalization for an interacting field, with the…
Gauge theory requires physical observables to be gauge-independent. However, ever since Lamb noticed the problem of gauge selection in calculating atomic spontaneous radiation spectrum, the problem of gauge dependence was encountered in…
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Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and…
A random recursive cell splitting scheme of the $2$-dimensional unit sphere is considered, which is the spherical analogue of the STIT tessellation process from Euclidean stochastic geometry. First-order moments are computed for a large…
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We review and study some of the properties of smooth Gaussian random fields defined on a homogeneous space, under the assumption that the probability distribution is invariant under the isometry group of the space. We first give an…
We analyze the transformation of quantum fields under conformal coordinate transformations from inertial to accelerated frames, in the simple case of scalar massless fields in a two-dimensional spacetime, through the transformation of…
Scalar cosmological perturbations with nearly flat power spectrum may originate from perturbations of the phase of a scalar field conformally coupled to gravity and rolling down negative quartic potential. We consider a version of this…
The linearized Einstein field equations with the renormalized stress tensor of a massless quantum scalar field as source are solved in the 4-dimensional spacetime near an infinite plane boundary. The motion of particles and light is…
The time-dependent electromagnetic field can results both pair waves and pair particles. It can be for mathematical relations between two functions with identical argument and difference of phases equal to $\pi$. Two examples both the…
A putative temporally varying circulation-free magnetic-field configuration is inferred in an equatorial segment of the solar convection zone from the helioseismologically inferred angular-velocity variation, assuming that the predominant…
We consider continuous time random interlacements on $\mathbb{Z}^d$, $d \ge 3$, and characterize the distribution of the corresponding stationary random field of occupation times. When d = 3, we relate this random field to the…
We construct a natural discrete random field on $\mathbb{Z}^{d}$, $d\geq 5$ that converges weakly to the bi-Laplacian Gaussian field in the scaling limit. The construction is based on assigning i.i.d. Bernoulli random variables on each…
The statistical translation invariance of cosmological random fields is broken by a finite survey boundary, correlating the observable Fourier modes. Standard methods for generating Gaussian fields either neglect these correlations, or are…
The classical Hamiltonian system of time-dependent harmonic oscillator driven by the arbitrary external time-dependent force is considered. Exact analytical solution of the corresponding equations of motion is constructed in the framework…
We study the cosmic evolution of the magnetic fields of a large sample of spiral galaxies in a cosmologically representative volume by employing a semi-analytic galaxy formation model and numerical dynamo solver in tandem. We start by…
Free field equations, with various spins, for space-time algebras with second-rank tensor (instead of usual vector) momentum are constructed. Similar algebras are appearing in superstring/M theories. The most attention is payed to the gauge…