Related papers: Simulation of Gaussian random field in a ball
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…
Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps. This opens the door for tools from computational algebraic geometry. These tools can be…
Spectral analysis plays a crucial role in high-dimensional statistics, where determining the asymptotic distribution of various spectral statistics remains a challenging task. Due to the difficulties of deriving the analytic form, recent…
Random fields in nature often have, to a good approximation, Gaussian characteristics. We present the mathematical framework for a new and simple method for investigating the non-Gaussian contributions, based on counting the maxima and…
We study the phase diagram of scalar field theory on a three dimensional Euclidean spacetime whose spatial component is a fuzzy sphere. The corresponding model is an ordinary one-dimensional matrix model deformed by terms involving fixed…
3D Gaussian Splatting (3DGS) enables high-fidelity real-time rendering, a key requirement for immersive applications. However, the extension of 3DGS to dynamic scenes remains limitations on the substantial data volume of dense Gaussians and…
We revisit the scaling properties of growing spheres randomly seeded in d=2,3 and 4 dimensions using a mean-field approach. We model the insertion probability without assuming a priori a functional form for the radius distribution. The…
Since its introduction, 3D Gaussian Splatting (3DGS) has rapidly transformed the landscape of 3D scene representations, inspiring an extensive body of associated research. Follow-up work includes analyses and contributions that enhance the…
Hard spheres are a central and important model reference system for both homogeneous and inhomogeneous fluid systems. In this paper we present new high-precision molecular-dynamics computer simulations for a hard sphere fluid at a planar…
A non-stationary spatial Gaussian random field (GRF) is described as the solution of an inhomogeneous stochastic partial differential equation (SPDE), where the covariance structure of the GRF is controlled by the coefficients in the SPDE.…
We develop the frame-like formulation of massive bosonic higher spins fields in the case of 3-dimensional $(A)dS$ space with the arbitrary cosmological constant. The formulation is based on gauge-invariant description by involving the…
We introduce statistical techniques required to handle complex computer models with potential applications to astronomy. Computer experiments play a critical role in almost all fields of scientific research and engineering. These computer…
A coherently oscillating real scalar field with potential shallower than quadratic one fragments into spherical objects called I-balls. We study the I-ball formation for logarithmic potential which appears in many cosmological models. We…
A new formalism is presented for analytically obtaining the probability density function, \( P_{n}(s) \), for the distance between two random points in an \( n \)-dimensional sphere of radius \( R \). Our formalism allows \( P_{n}(s) \) to…
Simulating the real-time dynamics of quantum field theories (QFTs) is one of the most promising applications of quantum simulators. Regularizing a bosonic QFT for quantum simulation purposes typically involves a truncation in Hilbert space…
We investigate the probability distribution function of the free flight time and of the number of collisions in a hard sphere gas at equilibrium. At variance with naive expectation, the latter quantity does not follow Poissonian statistics,…
Motivated by the subordinated Brownian motion, we define a new class of (in general discontinuous) random fields on higher-dimensional parameter domains: the subordinated Gaussian random field. We investigate the pointwise marginal…
In this paper we provide some simple characterizations for the spherical harmonics coefficients of an isotropic random field on the sphere. The main result is a characterization of isotropic gaussian fields through independence of the…
We introduce the model of inelastic hard spheres with random restitution coefficient $\alpha$, in order to account for the fact that, in a vertically shaken granular system interacting elastically with the vibrating boundary, the energy…
A method to reconstruct fields, source strengths and physical parameters based on Gaussian process regression is presented for the case where data are known to fulfill a given linear differential equation with localized sources. The…