Related papers: Gaussian random fields on the sphere and sphere cr…

We consider a class of Gaussian Free Fields denoted by $(g_x)_{x \in {\cal V}_N}$, where $ {\cal V}_N = \{0,1\}^N$ and $N\in \mathbb{Z}_+$. These fields are related to a general class of $N$-dimensional random walks on the hypercube, which…

We study the Boltzmann equation with hard sphere in a near-equilibrium setting. The initial data is compactly supported in the space variable and has a polynomial tail in the microscopic velocity. We show that the solution can be decomposed…

Surface transport of inertial particles is investigated by means of the perturbative approach, introduced by Maxey (J. Fluid Mech. 174, 441 (1987)), which is valid in the case the deflections induced on the particle trajectories by the…

We evaluate numerically the velocity field distributions produced by a bounded, two-dimensional fluid model consisting of a collection of parallel ideal line vortices. We sample at many spatial points inside a rigid circular boundary. We…

We consider modeling of angular or directional data viewed as a linear variable wrapped onto a unit circle. In particular, we focus on the spatio-temporal context, motivated by a collection of wave directions obtained as computer model…

We present a simple method to decompose the Green forms corresponding to a large class of interesting symmetric Dirichlet forms into integrals over symmetric positive semi-definite and finite range (properly supported) forms that are…

We introduce the (path-valued) Brownian frame process whose evaluation at time t is the sample path of the underlying Brownian motion run from time t-1 to t. Due to its connections with Gaussian Volterra processes and SDDEs this is an…

Smooth random Gaussian functions play an important role in mathematical physics, a main example being the random plane wave model conjectured by Berry to give a universal description of high-energy eigenfunctions of the Laplacian on generic…

Based on a re-formulation of the classical explanation of quantum mechanical Gaussian dispersion (Groessing et al. 2010) as well as interference of two Gaussians (Groessing et al. 2012), we present a new and more practical way of their…

In this paper, we consider a stochastic system described by a differential equation admitting a spatially varying random coefficient. The differential equation has been employed to model various static physics systems such as elastic…

The paper starts by giving a motivation for this research and justifying the considered stochastic diffusion models for cosmic microwave background radiation studies. Then it derives the exact solution in terms of a series expansion to a…

We consider the signed density of the extremal points of (two-dimensional) scalar fields with a Gaussian distribution. We assign a positive unit charge to the maxima and minima of the function and a negative one to its saddles. At first, we…

We study the small deviation probabilities of a family of very smooth self-similar Gaussian processes. The canonical process from the family has the same scaling property as standard Brownian motion and plays an important role in the study…

In this article we aim at defining the discrete Gaussian free field (DGFF) on a compact manifold. Since there is no canonical grid approximation of a manifold, we construct a random graph that suitably replaces the square lattice…

We prove a conjecture due to Sturmfels and Uhler concerning the degree of the projective variety associated to the Gaussian graphical model of the cycle. We involve new methods based on the intersection theory in the space of complete…

Spectral approximation and variational inducing learning for the Gaussian process are two popular methods to reduce computational complexity. However, in previous research, those methods always tend to adopt the orthonormal basis functions,…

We study analogies between the rational integers on the real line and the Gaussian integers on other lines in the complex plane. This includes a Gaussian analog of Bertrands Postulate, the Chinese Remainder Theorem, and the periodicity of…

We compute explicit upper bounds on the distance between the law of a multivariate Gaussian distribution and the joint law of wavelets/needlets coefficients based on a homogeneous spherical Poisson field. In particular, we develop some…

We consider the Busemann process in planar directed first passage percolation. We extend existing techniques to establish the existence of the process in our setting and determine its distribution in a number of integrable models. As…

We introduce a stochastic analysis of Grassmann random variables suitable for the stochastic quantization of Euclidean fermionic quantum field theories. Analysis on Grassmann algebras is developed here from the point of view of quantum…