Related papers: Spatial Form Factor for Point Patterns: Poisson Po…
This study investigates the spatial distribution of emergency alarm call events to identify spatial covariates associated with the events and discern hotspot regions for the events. The study is motivated by the problem of developing…
Identifying an appropriate covariance function is one of the primary interests in spatial and spatio-temporal statistics because it allows researchers to analyze the dependence structure of the random process. For this purpose, spatial…
We investigate spatial random graphs defined on the points of a Poisson process in $d$-dimensional space, which combine scale-free degree distributions and long-range effects. Every Poisson point is assigned an independent weight. Given the…
We review applications of factorization methods to the problem of finding stationary point vortex patterns in two-dimensional fluid mechanics. Then we present a new class of patterns related to periodic analogs of Schrodinger operators from…
Suppose that particles are randomly distributed in $\bR^d$, and they are subject to identical stochastic motion independently of each other. The Smoluchowski process describes fluctuations of the number of particles in an observation region…
We model the unidentified aerial phenomena observed in France during the last 60 years as a spatial point pattern. We use some public information such as population density, rate of moisture or presence of airports to model the intensity of…
Poisson point processes provide a versatile framework for modeling the distributions of random points in space. When the space is partitioned into cells, each associated with a single generating point from the Poisson process, there appears…
We consider square-integrable functionals of Poisson point processes for which the variance upper bound provided by the classical Poincar\'{e} inequality is suboptimal, a phenomenon known as superconcentration. In this paper, we establish a…
Over the last two decades, several fast, robust, and high-order accurate methods have been developed for solving the Poisson equation in complicated geometry using potential theory. In this approach, rather than discretizing the partial…
Fix a subset $S \subset \mathbb{R}^n$ of volume at most $c n$ that satisfies $S \cap (-S) = \emptyset$. We consider two point processes in $S$: the first is the Poisson point process of intensity one, and the second is the restriction of a…
In the theory of disordered systems the spectral form factor $S(\tau)$, the Fourier transform of the two-level correlation function with respect to the difference of energies, is linear for $\tau<\tau_c$ and constant for $\tau>\tau_c$. Near…
Advancements in theoretical and algorithmic approaches, workflow engines, and an ever-increasing computational power have enabled a novel paradigm for materials discovery through first-principles high-throughput simulations. A major…
In recent years there has been a lot of interest in the study of isometry invariant Poisson processes of $k$-flats in $d$-dimensional hyperbolic space $\mathbb{H}^d$, for $0\le k\le d-1$. A phenomenon that has no counterpart in euclidean…
This survey will appear as a chapter of the forthcoming book [19]. A U-statistic of order $k$ with kernel $f:\X^k \to \R^d$ over a Poisson process is defined in \cite{ReiSch11} as$$ \sum\_{x\_1, \dots , x\_k \in \eta^k\_{\neq}} f(x\_1,…
We consider a stationary spatio-temporal random process and assume that we have a sample. By defining a sequence of discrete Fourier transforms at canonical frequencies at each location, and using these complex valued random varables as…
We propose a geometric interpretation for the Stokes phenomenon in de Sitter spacetime that particles are produced in even dimensions but not in odd dimensions. The scattering amplitude for a quantum field between the in-vacuum and the…
A general problem of $2\rightarrow N_f$ scattering is addressed with all the states being wave packets with arbitrary phases. Depending on these phases, one deals with coherent states in $(3+1)$ D, vortex particles with orbital angular…
We study point processes on $\mathbb S^d$, the $d$-dimensional unit sphere $\mathbb S^d$, considering both the isotropic and the anisotropic case, and focusing mostly on the spherical case $d=2$. The first part studies reduced Palm…
The Stochastic Heat Flow (SHF) emerges as the scaling limit of directed polymers in random environments and the noise-mollified Stochastic Heat Equation (SHE), specifically at the critical dimension of two and near the critical temperature.…
This paper is focused on a class of spatial birth and death process of the Euclidean space where the birth rate is constant and the death rate of a given point is the shot noise created at its location by the other points of the current…