Related papers: Space-Time Models based on Random Fields with Loca…
We derive the interaction of fermions with a dynamical space-time based on the postulate that the description of physics should be independent of the reference frame, which means to require the form-invariance of the fermion action under…
We present a way of understanding the curvature of space-time, the basic philosophy being that the (linear) geometry of any space is determined by the (linear) functionals on the algebra(s) of any fields defined on the space. It is known…
We develop two statistical models for space-time abundance data based on a stochastic underlying continuous individual movement. In contrast to current models for abundance in statistical ecology, our models exploit the explicit connection…
We propose a new approximation-technique to deal with the exact macroscopic integro-differential evolution equations of statistical systems which self-consistently accounts for dissipative effects. Concentrating on one and two point…
Stochastic models for spatio-temporal transport face a critical trade-off between physical realism and interpretability. The advection model with a single constant velocity is interpretable but physically limited by its perfect correlation…
Linear diffusions are used to model a large number of stochastic processes in physics, including small mechanical and electrical systems perturbed by thermal noise, as well as Brownian particles controlled by electrical and optical forces.…
A stochastic field theory approach is applied to a coarse-grained polymer model that will enable studies of polymer behavior under non-equilibrium conditions. This article is focused on the validation of the new model in comparison to…
In stochastic quantisation, quantum mechanical expectation values are computed as averages over the time history of a stochastic process described by a Langevin equation. Complex stochastic quantisation, though theoretically not rigorously…
We develop a technique for finding the dynamical evolution in time of an averaged density matrix. The result is an equation of evolution that includes an Effective Hamiltonian, as well as decoherence terms in Lindblad form. Applying the…
Spatial prediction problems often use Gaussian process models, which can be computationally burdensome in high dimensions. Specification of an appropriate covariance function for the model can be challenging when complex non-stationarities…
Nonstationary Gaussian processes (GPs) are essential for modeling complex, locally heterogeneous spatial data. A common modeling approach is the spatial deformation method that warps the domain to recover isotropy. However, this static…
Dynamic heterogeneity has often been modeled by assuming that a single-particle observable, fluctuating at a molecular scale, is influenced by its coupling to environmental variables fluctuating on a second, perhaps slower, time scale.…
Stochastic evolutions of classical field theories have recently become popular in the study of problems such as determination of the rates of topological transitions and the statistical mechanics of nonlinear coherent structures. To obtain…
We derive a time-dependent density functional theory appropriate for calculating the near-edge X-ray absorption spectrum in molecules and condensed matter. The basic assumption is to increase the space of many-body wave functions from one…
We treat a relativistically moving particle interacting with a quantum field from an open system viewpoint of quantum field theory by the method of influence functionals or closed-time-path coarse-grained effective actions. The particle…
We consider a hypothesis in which classical space-time emerges from information exchange (interactions) between quantum fluctuations in the gravity theory. In this picture, a line element would arise as a statistical average of how…
An important class of spatio-temporal models is constructed by leveraging the hierarchical structure of dynamical (or, state-space) models. This paper proposes a new statistical dynamical model for spatio-temporal processes motivated by…
Hamiltonian gravity, relying on arbitrary choices of "space," can obscure spacetime symmetries. We present an alternative, manifestly spacetime covariant formulation that nonetheless distinguishes between "spatial" and "temporal" variables.…
The stochastic solution with Gaussian stationary increments is establihsed for the symmetric space-time fractional diffusion equation when $0 < \beta < \alpha \le 2$, where $0 < \beta \le 1$ and $0 < \alpha \le 2$ are the fractional…
Multivariate spatial-statistical models are often used when modeling environmental and socio-demographic processes. The most commonly used models for multivariate spatial covariances assume both stationarity and symmetry for the…