Zobrazeno 1 - 10
of 119
pro vyhledávání: '"60D05 60F05"'
Consider a stationary Poisson process $\eta$ in the $d$-dimensional Euclidean or hyperbolic space and construct a random graph with vertex set $\eta$ as follows. First, each point $x\in\eta$ is connected by an edge to its nearest neighbour, then to i
Externí odkaz:
http://arxiv.org/abs/2411.00748
We consider large uniform random trees where we fix for each vertex its degree and height. We prove, under natural conditions of convergence for the profile, that those trees properly renormalized converge. To this end, we study the paths from random
Externí odkaz:
http://arxiv.org/abs/2409.12897
In this paper, we introduce a novel model for random hypergraphs based on weighted random connection models. In accordance with the standard theory for hypergraphs, this model is constructed from a bipartite graph. In our stochastic model, both verte
Externí odkaz:
http://arxiv.org/abs/2407.16334
Autor:
Penrose, Mathew D., Higgs, Frankie
Given a compact planar region $A$, let $\tau_A$ be the (random) time it takes for $A$ to be fully covered by a spatial birth-growth process in $A$ with seeds arriving as a unit-intensity Poisson point process in $A \times [0,\infty)$, where upon arri
Externí odkaz:
http://arxiv.org/abs/2405.17687
In this paper, we study the limiting behavior of the perimeter and diameter functionals of the convex hull spanned by the first $n$ steps of two planar random walks. As the main results, we obtain the strong law of large numbers and the central limit
Externí odkaz:
http://arxiv.org/abs/2403.17705
We study the connected components in critical percolation on the Hamming hypercube $\{0,1\}^m$. We show that their sizes rescaled by $2^{-2m/3}$ converge in distribution, and that, considered as metric measure spaces with the graph distance rescaled
Externí odkaz:
http://arxiv.org/abs/2401.16365
Let $X_1,X_2, \ldots $ and $Y_1, Y_2, \ldots$ be i.i.d. random uniform points in a bounded domain $A \subset \mathbb{R}^2$ with smooth or polygonal boundary. Given $n,m,k \in \mathbb{N}$, define the {\em two-sample $k$-coverage threshold} $R_{n,m,k}$
Externí odkaz:
http://arxiv.org/abs/2401.03832
Autor:
Fodor, Ferenc, Papvári, Dániel I.
In this paper we prove a quantitative central limit theorem for the area of uniform random disc-polygons in smooth convex discs whose boundary is $C^2_+$. We use Stein's method and the asymptotic lower bound for the variance of the area proved by Fod
Externí odkaz:
http://arxiv.org/abs/2310.18143
We investigate scaling limits of trees built by uniform attachment with freezing, which is a variant of the classical model of random recursive trees introduced in a companion paper. Here vertices are allowed to freeze, and arriving vertices cannot b
Externí odkaz:
http://arxiv.org/abs/2308.00484
Autor:
Lemoine, Thibaut
We study determinantal point processes whose correlation kernel is the Bergman kernel of a high power of a positive Hermitian holomorphic line bundle over a compact complex manifold. We construct such processes in analogy to the orthogonal ensembles
Externí odkaz:
http://arxiv.org/abs/2211.06955