Zobrazeno 1 - 10
of 3 829
pro vyhledávání: '"05C80"'
We consider general continuum percolation models obeying sparseness, translation invariance, and spatial decorrelation. In particular, this includes models constructed on general point sets other than the standard Poisson point process or the Bernoul
Externí odkaz:
http://arxiv.org/abs/2411.10333
Autor:
Richland, Joshua, Strang, Alexander
We analyze the correlation between randomly chosen edge weights on neighboring edges in a directed graph. This shared-endpoint correlation controls the expected organization of randomly drawn edge flows when the flow on each edge is conditionally ind
Externí odkaz:
http://arxiv.org/abs/2411.06314
In group testing, the task is to identify defective items by testing groups of them together using as few tests as possible. We consider the setting where each item is defective with a constant probability $\alpha$, independent of all other items. In
Externí odkaz:
http://arxiv.org/abs/2411.03839
In this article, we derive Stein's method for approximating a spatial random graph by a generalised random geometric graph, which has vertices given by a finite Gibbs point process and edges based on a general connection function. Our main theorems p
Externí odkaz:
http://arxiv.org/abs/2411.02917
Autor:
de Lima, Lucas R., Valesin, Daniel
This study delves into first-passage percolation (FPP) on random geometric graphs (RGGs) in the supercritical regime, where RGGs feature a unique infinite connected component. We investigate properties such as geodesic paths, moderate deviations, and
Externí odkaz:
http://arxiv.org/abs/2411.02046
Autor:
Iyer, Tejas
A sequence of trees $(\mathcal{T}_{n})_{n \in \mathbb{N}}$ contains a \emph{persistent hub}, or displays \emph{degree centrality}, if there is a fixed node of maximal degree for all sufficiently large $n \in \mathbb{N}$. We derive sufficient criteria
Externí odkaz:
http://arxiv.org/abs/2410.24170
Both empirical and theoretical investigations of scale-free network models have found that large degrees in a network exert an outsized impact on its structure. However, the tools used to infer the tail behavior of degree distributions in scale-free
Externí odkaz:
http://arxiv.org/abs/2410.22703
We consider the graphical representations of the Ising model on tree-like graphs. We construct a class of graphs on which the loop $\mathrm{O}(1)$ model and then single random current exhibit a non-unique phase transition with respect to the inverse
Externí odkaz:
http://arxiv.org/abs/2410.22061
We present a stochastic model for two successive SIR (Susceptible, Infectious, Recovered) epidemics in the same network structured population. Individuals infected during the first epidemic might have (partial) immunity for the second one. The first
Externí odkaz:
http://arxiv.org/abs/2410.20889
Autor:
Krishnan, Neil, Li, Rupert
Friends-and-strangers graphs, coined by Defant and Kravitz, are denoted by $\mathsf{FS}(X,Y)$ where $X$ and $Y$ are both graphs on $n$ vertices. The graph $X$ represents positions and edges mark adjacent positions while the graph $Y$ represents peopl
Externí odkaz:
http://arxiv.org/abs/2410.21334