Related papers: Star-collision in random hypergraphs
The $2$-star model is the simplest exponential random graph model that displays complex behavior, such as degeneracy and phase transition. Despite its importance, this model has been solved only in the regime of dense connectivity. In this…
What is the difference between a long-lived unstable (or quasi-stable) multiple star system and a bona fide star cluster? In this paper, we present a possible framework to address this question, by studying the distributions of disruption…
We study the asymptotic behavior of the number of paths of length $N$ on several classes of infinite graphs with a single special vertex. This vertex can work as an entropic trap for the path, i.e. under certain conditions the dominant part…
Galactic collisions are normally modeled in a CDM model by assuming the DM consists of a small number of very massive objects. This note shows that the behaviour of a CDM halo during collisions depends critically on the mass of the…
An r-cut of a k-uniform hypergraph H is a partition of the vertex set of H into r parts and the size of the cut is the number of edges which have a vertex in each part. A classical result of Edwards says that every m-edge graph has a 2-cut…
We study the algebra of upper triangular matrices endowed with a group grading and a homogeneous involution over an infinite field. We compute the asymptotic behaviour of its (graded) star-codimension sequence. It turns out that the…
The stable matching problem is a prototype model in economics and social sciences where agents act selfishly to optimize their own satisfaction, subject to mutually conflicting constraints. A stable matching is a pairing of adjacent…
We develop a general formalism to treat, in general relativity, the nonradial oscillations of a superfluid neutron star about static (non-rotating) configurations. The matter content of these stars can, as a first approximation, be…
We consider the effects of large structures in the Universe on the Hubble diagram. This problem is treated non-linearly by considering a Swiss Cheese model of the Universe in which under-dense voids are represented as negatively curved…
Non-equilibrium steady states of quantum fields on star graphs are explicitly constructed. These states are parametrized by the temperature and the chemical potential, associated with each edge of the graph. Time reversal invariance is…
The early evolution of dense star clusters is possibly dominated by close interactions between stars, and physical collisions between stars may occur quite frequently. Simulating a stellar collision event can be an intensive numerical task,…
A sequence of large invertible matrices given by a small random perturbation around a fixed diagonal and positive matrix induces a random dynamics on a high-dimensional sphere. For a certain class of rotationally invariant random…
We study the susceptibility, i.e., the mean size of the component containing a random vertex, in a general model of inhomogeneous random graphs. This is one of the fundamental quantities associated to (percolation) phase transitions; in…
The basic interaction unit of many dynamical systems involves more than two nodes. In such situations where networks are not an appropriate modelling framework, it has recently become increasingly popular to turn to higher-order models,…
Let $r \ge 2$ be a fixed constant and let $ {\mathcal H}$ be an $r$-uniform, $D$-regular hypergraph on $N$ vertices. Assume further that $ D \to \infty$ as $N \to \infty$ and that degrees of pairs of vertices in ${\mathcal H}$ are at most…
The centres of galaxies host nuclear stellar clusters, supermassive black holes, or both. The origin of this dichotomy is still a mystery. Nuclear stellar clusters are the densest stellar system in the Universe, so they are ideal places for…
We explore various instability models for the onset of star formation in irregular galaxies. Critical gas densities are calculated for gravitational instabilities with a thin, pure-gas disk, and with a thick disk composed of gas and a…
Planet-planet collisions are a common outcome of instability in systems of transiting planets close to the star, as well as occurring during in-situ formation of such planets from embryos. Previous N-body studies of instability amongst…
A map is given showing that convolutions of independent random variables over a finite group and matrix multiplications of doubly stochastic matrices are homomorphic. As an application, a short proof is given to the theorem that the…
We present the second paper in our program characterizing the impact of massive neutrinos on the multiscale cosmic web using global topology and persistent homology. Building on the methodology established in Paper I, based on discrete…