Related papers: Distribution of Transverse Distances in Directed A…
In this paper, we use the framework of mod-$\phi$ convergence to prove precise large or moderate deviations for quite general sequences of real valued random variables $(X_{n})_{n \in \mathbb{N}}$, which can be lattice or non-lattice…
Several representations of the exact cdf of the sum of squares of n independent gamma-distributed random variables Xi are given, in particular by a series of gamma distribution functions. Using a characterization of the gamma distribution…
We prove that the growth constants for nearest-neighbour lattice trees and lattice (bond) animals on the integer lattice Zd are asymptotic to 2de as the dimension goes to infinity, and that their critical one-point functions converge to e.…
We prove that in the full $L^2$-regime the partition function of the directed polymer model in dimensions $d\geq 3$, if centered, scaled and averaged with respect to a test function $\varphi \in C_c(\mathbb{R}^d)$, converges in distribution…
We prove a novel result wherein the density function of the gradients---corresponding to density function of the derivatives in one dimension---of a thrice differentiable function S (obtained via a random variable transformation of a…
We consider the inverse elastic scattering of incident plane compressional and shear waves from the knowledge of the far field patterns. Specifically, three direct sampling methods for location and shape reconstruction are proposed using…
Though smooth, extended spheroidal stellar outskirts have long been observed around nearby dwarf galaxies, it is unclear whether dwarfs generically host an extended stellar halo. We use imaging from the Hyper Suprime-Cam Subaru Strategic…
We analyze diffusion of particles on a two dimensional square lattice. Each lattice site contains an arbitrary number of particles. Interactions affect particles only in the same site, and are macroscopically represented by the excess…
A function $f: \mathbb{R}^d \rightarrow \mathbb{R}$ is referred to as a Sparse Additive Model (SPAM), if it is of the form $f(\mathbf{x}) = \sum_{l \in \mathcal{S}}\phi_{l}(x_l)$, where $\mathcal{S} \subset [d]$, $|\mathcal{S}| \ll d$.…
We study a symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are…
Starting from a simple animal-biology example, a general, somewhat counter-intuitive property of diffusion random walks is presented. It is shown that for any (non-homogeneous) purely diffusing system, under any isotropic uniform incidence,…
We perform numerical simulations of the lattice-animal problem at the upper critical dimension d=8 on hypercubic lattices in order to investigate logarithmic corrections to scaling there. Our stochastic sampling method is based on the…
We investigate the amount of scatter in the Tully-Fisher relation (TFR) when using optical long-slit H-alpha rotation curves to determine the velocity widths of spiral galaxies. We study a sample of 25 galaxies in the Coma region of the sky…
We compute the gap distribution of directions of saddle connections for two classes of translation surfaces. One class will be the translation surfaces arising from gluing two identical tori along a slit. These yield the first explicit…
We model the shape and spin characteristics of an object population when there are not enough data to model its single members. The data are random projection areas of the members. We construct a mapping $f(x)\rightarrow C(y)$,…
We experimentally probe the vicinity of the jamming point J, located at a density $\phi$ corresponding to random close packing ($\phi_{rcp} = 0.842$), in two dimensional, bidisperse packings of foam bubbles. We vary the density of the foam…
We study the $1+1$-dimensional random directed polymer problem, i.e., an elastic string $\phi(x)$ subject to a Gaussian random potential $V(\phi,x)$ and confined within a plane. We mainly concentrate on the short-scale and…
We report that Ly$\alpha$-emitting galaxies (LAEs) may not faithfully trace the cosmic web of neutral hydrogen (HI), but their distribution is likely biased depending on the viewing direction. We calculate the cross-correlation (CCF)…
A spread-out lattice animal is a finite connected set of edges in $\{ \{x,y\} \subset \mathbb{Z}^d:0<||x-y||\le L \}$. A lattice tree is a lattice animal with no loops.The best estimate on the critical point $p_c$ so far was achieved by…
We propose a new approach to visual perception for relative localization of agents within large-scale swarms of UAVs. Inspired by biological perception utilized by schools of sardines, swarms of bees, and other large groups of animals…