Related papers: Atypical stars on a directed landscape geodesic

Stars form in molecular complexes that are visible as giant clouds ($\sim 10^{5-6} \mathrm{M}_\odot$) in nearby galaxies and as giant clumps ($\sim 10^{8-9}\mathrm{M}_\odot$) in galaxies at redshifts $z\approx1$$-$$3$. Theoretical…

The trace anomaly $\Delta\equiv 1/3-P/\varepsilon=1/3-\phi$ quantifies the possibly broken conformal symmetry in supradense matter under pressure $P$ at energy density $\varepsilon$. Perturbative QCD (pQCD) predicts a vanishing $\Delta$ at…

We investigate first-passage percolation on the lattice $\Z^d$ for dimensions $d \geq 2$. Each edge $e$ of the graph is assigned an independent copy of a non-negative random variable $\tau$. We only assume $\P[\tau=0]0$ is explicit) for the…

Two-dimensional networks of ordered quantum dots beyond the percolation threshold are studied, as typical example of conducting nanostructures with quenched random disorder. Theory predicts anomalous diffusion with stretched-exponential…

We study the asymptotics of large directed graphs, constrained to have certain densities of edges and/or outward $p$-stars. Our models are close cousins of exponential random graph models (ERGMs), in which edges and certain other subgraph…

We developed a code that estimates distances to stars using measured spectroscopic and photometric quantities. We employ a Bayesian approach to build the probability distribution function over stellar evolutionary models given these data,…

Models of discrete space and space-time that exhibit continuum-like behavior at large lengths could have profound implications for physics. They may tame the infinities that arise from quantizing gravity, and dispense with the machinery of…

In this article a collection of random self-similar fractal dendrites is constructed, and their Hausdorff dimension is calculated. Previous results determining this quantity for random self-similar structures have relied on geometrical…

Using the stellar photometry catalogue based on the latest data release (DR4) of the Sloan Digital Sky Survey (SDSS), a study of the Galactic structure using star counts is carried out for selected areas of the sky. The sample areas are…

Two-dimensional quantum gravity, defined either via scaling limits of random discrete surfaces or via Liouville quantum gravity, is known to possess a geometry that is genuinely fractal with a Hausdorff dimension equal to 4. Coupling…

In addition to occupying the extreme, diffuse tail of the dwarf galaxy population, Ultra-Diffuse Galaxies (UDGs) are themselves a key laboratory in which to study star formation in extreme low-density environments. In the second paper of…

We consider fixed-point equations for probability distributions on isometry classes of measured metric spaces. The construction is required to be recursive and tree-like, but we allow loops for the geodesics between points in the support of…

Let Z be a so-called well-behaved percolation, i.e. a certain random closed set in the hyperbolic plane, whose law is invariant under all isometries; for example the covered region in a Poisson Boolean model. The Hausdorff-dimension of the…

(Abridged). We model gravitational instability in a wide range of isolated disk galaxies, using GADGET, a three-dimensional, smoothed particle hydrodynamics code. The model galaxies include a dark matter halo and a disk of stars and…

We show that compact embedded starshaped $r$-convex hypersurfaces of certain warped products satisfying $H_r=aH+b$ with $a\geqslant 0$, $b>0$, where $H$ and $H_r$ are respectively the mean curvature and $r$-th mean curvature is a slice. In…

Let $X = G/\Gamma$, where $G$ is a Lie group and $\Gamma$ is a lattice in $G$, let $O$ be an open subset of $X$, and let $F = \{g_t: t\ge 0\}$ be a one-parameter subsemigroup of $G$. Consider the set of points in $X$ whose $F$-orbit misses…

In the present paper, we report on a study of the anisotropic strange stars under Finsler geometry. Keeping in mind that Finsler spacetime is not merely a generalization of Riemannian geometry rather the main idea is the projectivized…

In this article we propose a generalization of the 2-dimensional notions of convexity resp. being star-shaped to symplectic vector spaces. We call such curves symplectically convex resp. symplectically star-shaped. After presenting some…

Stars are not perfectly spherically symmetric. They are deformed by rotation and magnetic fields. Until now, the study of stellar shapes has only been possible with optical interferometry for a few of the fastest-rotating nearby stars. We…

We study $k$-star decompositions, that is, partitions of the edge set into disjoint stars with $k$ edges, in the uniformly random $d$-regular graph model $\mathcal{G}_{n,d}$. Using the small subgraph conditioning method, we prove an…