Zobrazeno 1 - 10
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pro vyhledávání: '"60D05"'
Autor:
Ewers, Emily, Turova, Tatyana
A random planar quadrangulation process is introduced as an approximation for certain cellular automata describing neuronal dynamics. This model turns out to be a particular (rectangular) case of a well-known Gilbert tessellation. The central and sti
Externí odkaz:
http://arxiv.org/abs/2412.04212
Autor:
Kammerer, Emmanuel
We establish the scaling limit of the geodesics to the root for the first passage percolation distance on random planar maps. We first describe the scaling limit of the number of faces along the geodesics. This result enables to compare the metric ba
Externí odkaz:
http://arxiv.org/abs/2412.02666
Autor:
D'Achille, Matteo
We construct and study the ideal Poisson--Voronoi tessellation of the product of two hyperbolic planes $\mathbb{H}_{2}\times \mathbb{H}_{2}$ endowed with the $L^{1}$ norm. We prove that its law is invariant under all isometries of this space and stud
Externí odkaz:
http://arxiv.org/abs/2412.00822
We investigate the asymptotic properties of random polytopes arising as convex hulls of $n$ independent random points sampled from a family of block-beta distributions. Notably, this family includes the uniform distribution on a product of Euclidean
Externí odkaz:
http://arxiv.org/abs/2411.19163
In this paper we propose and study a class of nonparametric, yet interpretable measures of association between two random vectors $X$ and $Y$ taking values in $\mathbb{R}^{d_1}$ and $\mathbb{R}^{d_2}$ respectively ($d_1, d_2\ge 1$). These nonparametr
Externí odkaz:
http://arxiv.org/abs/2411.13080
Autor:
Mathis, Léo
We study the expected number of solutions of a system of identically distributed exponential sums with centered Gaussian coefficient and arbitrary variance. We use the Adler and Taylor theory of Gaussian random fields to identify a moment map which a
Externí odkaz:
http://arxiv.org/abs/2411.11345
Pick $n$ independent and uniform random points $U_1,\ldots,U_n$ in a compact convex set $K$ of $\mathbb{R}^d$ with volume 1, and let $P^{(d)}_K(n)$ be the probability that these points are in convex position. The Sylvester conjecture in $\mathbb{R}^d
Externí odkaz:
http://arxiv.org/abs/2411.08456
Autor:
Krishnapur, Manjunath, Yogeshwaran, D.
We consider covariance asymptotics for linear statistics of general stationary random measures in terms of their truncated pair correlation measure. We give exact infinite series-expansion formulas for covariance of smooth statistics of random measur
Externí odkaz:
http://arxiv.org/abs/2411.08848
Autor:
Kammerer, Emmanuel
We prove that for $n = 2$ the gaskets of critical rigid O(n) loop-decorated random planar maps are $3/2$-stable maps. The case $n = 2$ thus corresponds to the critical case in random planar maps. The proof relies on the Wiener-Hopf factorisation for
Externí odkaz:
http://arxiv.org/abs/2411.05541
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