Related papers: Strong Spatial Mixing for Binary Markov Random Fie…
We consider dynamical systems on a finite measure space fulfilling a spectral gap property and Birkhoff sums of a non-negative, non-integrable observable. For such systems we generalize strong laws of large numbers for intermediately…
In this paper, we consider the direct and inverse problems of the description of lattice positive random fields by various systems of finite-dimensional (as well as one-point) probability distributions parameterized by boundary conditions.…
We give some basic properties of strongly topologically transitive, supermixing, and hypermixing maps on general topological spaces. Then we present some other results for which our mappings need to be continuous.
Multivariate extreme value distributions are a common choice for modelling multivariate extremes. In high dimensions, however, the construction of flexible and parsimonious models is challenging. We propose to combine bivariate max-stable…
In this paper, we investigate the law of large numbers for strictly stationary random fields, that is, we provide sufficient conditions on the moments and the dependence of the random field in order to guarantee the almost sure convergence…
We solve the general problem of mixing of electromagnetic and scalar or pseudoscalar fields coupled by axion-type interactions ${\cal L}_{int} =g_{\phi} \phi \epsilon_{\mu \nu \a \b}F^{\mu \nu}F^{\a \b} $. The problem depends on several…
This paper investigates Gaussian Markov random field approximations to nonstationary Gaussian fields using graph representations of stochastic partial differential equations. We establish approximation error guarantees building on the…
A significant fraction of massive stars are found in multiple systems. The effect of binarity on stellar evolution is poorly constrained. In particular, the role of tides and mass transfer on surface chemical abundances is not constrained…
We study the effect of a sharply localized magnetic field on the electron transport in a strip (ribbon) of graphene sheet, which allows to give results for the transmission and reflection probability through magnetic barriers. The magnetic…
Discrete Markov random fields form a natural class of models to represent images and spatial data sets. The use of such models is, however, hampered by a computationally intractable normalising constant. This makes parameter estimation and…
We investigate the effects of pseudoscalar-photon mixing on electromagnetic radiation in the presence of correlated extragalactic magnetic fields. We model the Universe as a collection of magnetic domains and study the propagation of…
Within a lattice model describing a binary mixture with fixed concentrations of the species we discuss the relation-ship between the surface tension of the mixture and the concentrations.
The process of photon splitting $\gamma \to \gamma \gamma$ in a strong magnetic field is investigated both below and above the pair creation threshold. Contrary to the statement by Baier et al., the ``allowed'' channel $\alw$ is shown not…
We consider mixed configurations consisting of a wormhole filled by a strongly magnetized isotropic or anisotropic neutron fluid. The nontrivial topology of the spacetime is allowed by the presence of exotic matter. By comparing these…
In this review-type paper written at the occasion of the Oberwolfach workshop {\em One-sided vs. Two-sided stochastic processes} (february 22-29, 2020), we discuss and compare Markov properties and generalisations thereof in more…
We study the interaction of gauge fields of arbitrary integer spins with the constant electromagnetic field. We reduce the problem of obtaining the gauge-invariant Lagrangian of integer spin fields in the external field to purely algebraic…
We study conditional independence relationships for random networks and their interplay with exchangeability. We show that, for finitely exchangeable network models, the empirical subgraph densities are maximum likelihood estimates of their…
The particle Gibbs (PG) sampler is a systematic way of using a particle filter within Markov chain Monte Carlo (MCMC). This results in an off-the-shelf Markov kernel on the space of state trajectories, which can be used to simulate from the…
Let $\{X_{\mathbf{n}} : \mathbf{n}\in\mathbb{Z}^d\}$ be a weakly dependent stationary field with maxima $M_{A} := \sup\{X_{\mathbf{i}} : \mathbf{i}\in A\}$ for finite $A\subset\mathbb{Z}^d$ and $M_{\mathbf{n}} := \sup\{X_{\mathbf{i}} :…
This paper considers a Bayesian view for estimating a sub-network in a Markov random field. The sub-network corresponds to the Markov blanket of a set of query variables, where the set of potential neighbours here is big. We factorize the…