Related papers: Gaussian fields and random packing

Coincidence probabilities, which yield Renyi entropies, are investigated in a generalized Gaussian model, which includes interparticle correlations

We generate random functions locally via a novel generalization of Dyson Brownian motion, such that the functions are in a desired differentiability class, while ensuring that the Hessian is a member of the Gaussian orthogonal ensemble…

Motivated by a recently identified severe discrepancy between a static and a dynamic theory of glasses, we numerically investigate the behavior of dense hard spheres in spatial dimensions 3 to 12. Our results are consistent with the static…

We investigate the properties of a model of granular matter consisting of $N$ Brownian particles on a line subject to inelastic mutual collisions. This model displays a genuine thermodynamic limit for the mean values of the energy and the…

We present a statistical mechanical description of randomly packed spherical particles, where the average coordination number is treated as a macroscopic thermodynamic variable. The overall packing entropy is shown to have two…

Completing the study initiated by Mounaix and Collet [J. Stat. Phys. {\bf 143}, 139-147 (2011)], we investigate the realizations of a Gaussian random field in the limit where a given (general) quadratic form of the field is large.…

Double generalized linear models provide a flexible framework for modeling data by allowing the mean and the dispersion to vary across observations. Common members of the exponential dispersion family including the Gaussian, Poisson,…

The distributions of $ N $-particle systems of Gaussian unitary ensembles converge to Sine$_2$ point processes under bulk-scaling limits. These scalings are parameterized by a macro-position $ \theta $ in the support of the semicircle…

Spatial fields in the Earth and environmental sciences are often available at multiple scales or resolutions. While coarse-scale data (e.g., from global circulation models) are often abundant, they lack the local detail provided by…

We give an overview of the recent asymptotic results on the geometry of excursion sets of stationary random fields. Namely, we cover a number of limit theorems of central type for the volume of excursions of stationary (quasi--, positively…

Measurements of a weighted energy density average taken in the vacuum state of a conformal field theory in $1+1$ dimensions are randomly distributed with vanishing expectation value. The probability distribution is computed in closed form…

Various phenomenological models of particle multiplicity distributions are discussed using a general form of the grand canonical partition function. These phenomenological models include a wide range of varied processes such as coherent…

We consider a deposition model in which balls rain down at random towards a 2-dimensional surface, roll downwards over existing adsorbed balls, are adsorbed if they reach the surface, and discarded if not. We prove a spatial law of large…

The paper investigates uniform convergence of wavelet expansions of Gaussian random processes. The convergence is obtained under simple general conditions on processes and wavelets which can be easily verified. Applications of the developed…

Calculation of the distribution of the average value of a Gaussian random field in a finite domain is carried out for different cases. The results of the calculation demonstrate a strong dependence of the width of the distribution on the…

We propose an aggregated random-field model, and investigate the scaling limits of the aggregated partial-sum random fields. In our model, each copy of the random field in the aggregation is built from two correlated one-dimensional random…

We introduce and simulate a two dimensional probabilistic model of granular matter at vanishing pressure. The model exhibits a perfectly sharp random loose packing density, a phenomenon that should be verifiable for real granular matter.

We introduce a new method from number fields and codes to construct dense packings in the Euclidean spaces. Via the canonical $\mathbb{Q}$-embedding of arbitrary number field $K$ into $\mathbb{R}^{[K:\mathbb{Q}]}$, both the prime ideal…

The most efficient way to pack equally sized spheres isotropically in 3D is known as the random close packed state, which provides a starting point for many approximations in physics and engineering. However, the particle size distribution…

We present a Gaussian ensemble of random cyclic matrices on the real field and study their spectral fluctuations. These cyclic matrices are shown to be pseudo-symmetric with respect to generalized parity. We calculate the joint probability…