Výsledky vyhledávání - "Pierre Calka"

Poisson–Voronoi Tessellation on a Riemannian Manifold

Autor: Pierre Calka, Nathanaël Enriquez, Aurélie Chapron

Publikováno v: International Mathematics Research Notices. 2021:5413-5459

In this paper, we consider a Riemannian manifold $M$ and the Poisson–Voronoi tessellation generated by the union of a fixed point $x_0$ and a Poisson point process of intensity $\lambda $ on $M$. We obtain a two-term asymptotic expansion, when $\la

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::161b1ab822fccadae7792e0b9b5a0ee8
https://doi.org/10.1093/imrn/rnz357

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Convex hulls of perturbed random point sets

Autor: Joseph E. Yukich, Pierre Calka

Publikováno v: The Annals of Applied Probability. 31

We consider the convex hull of the perturbed point process comprised of $n$ i.i.d. points, each distributed as the sum of a uniform point on the unit sphere $\S^{d-1}$ and a uniform point in the $d$-dimensional ball centered at the origin and of radi

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https://doi.org/10.1214/20-aap1627

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Variance asymptotics and scaling limits for random polytopes

Autor: Pierre Calka, Joseph E. Yukich

Publikováno v: Advances in Mathematics. 304:1-55

Let K be a convex set in R d and let K λ be the convex hull of a homogeneous Poisson point process P λ of intensity λ on K. When K is a simple polytope, we establish scaling limits as λ → ∞ for the boundary of K λ in a vicinity of a vertex o

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::7776eff2db160114eaa0c65ce8ab83e7
https://doi.org/10.1016/j.aim.2016.08.006

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Mosaïque de Poisson-Voronoi sur une surface

Autor: Aurélie Chapron, Pierre Calka, Nathanaël Enriquez

Publikováno v: Séminaire de Probabilités L
Springer, Cham. Séminaire de Probabilités L, 2252, pp.9-16, 2019, Lecture Notes in Mathematics, 978-3-030-28534-0. ⟨10.1007/978-3-030-28535-7_3⟩
Lecture Notes in Mathematics ISBN: 9783030285340

L’objet de cette note est d’indiquer la maniere dont on peut etendre au cas d’une surface S, le celebre resultat, trouve independamment par Meijering en 1953 et Gilbert en 1962 , enoncant que le nombre moyen de sommets d’une cellule ou de fac

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::474265fd0801ebdcf6581b57412ef2d7
https://hal.archives-ouvertes.fr/hal-02377527

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Some Classical Problems in Random Geometry

Autor: Pierre Calka

Publikováno v: Stochastic geometry
Stochastic geometry, 2237, pp.1-43, 2019, Lecture Notes in Mathematics, 978-3-030-13546-1. ⟨10.1007/978-3-030-13547-8_1⟩
Stochastic Geometry ISBN: 9783030135461

International audience; This chapter is intended as a first introduction to selected topics in random geometry. It aims at showing how classical questions from recreational mathematics can lead to the modern theory of a mathematical domain at the int

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d78ed5c4fc958c4937247435e7149914
https://hal.archives-ouvertes.fr/hal-02377523/document

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Stochastic Geometry: Boolean model and random geometric graphs

Autor: Pierre Calka, Arnaud Rousselle, Anaïs Vergne, Jean-Baptiste Gouéré, David Coupier

Publikováno v: ESAIM: Proceedings and Surveys
ESAIM: Proceedings and Surveys, EDP Sciences, 2015, Modélisation Aléatoire et Statistique-Journées MAS 2014, 51, pp.175-192
ESAIM: Proceedings and Surveys, 2015, Modélisation Aléatoire et Statistique-Journées MAS 2014, 51, pp.175-192
ESAIM: Proceedings and Surveys, Vol 51, Pp 175-192 (2015)

This paper collects the four contributions which were presented during the session devoted to Stochastic Geometry at the journées MAS 2014. It is focused in particular on several questions related to the transmission of information in a general sens

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6599c55f0c1f3f97ff51b42611516b41
https://doi.org/10.1051/proc/201551010

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Variance asymptotics and scaling limits for Gaussian polytopes

Autor: Joseph E. Yukich, Pierre Calka

Publikováno v: Probability Theory and Related Fields. 163:259-301

Let $K_n$ be the convex hull of i.i.d. random variables distributed according to the standard normal distribution on $\mathbb {R}^d$. We establish variance asymptotics as $n \rightarrow \infty $ for the re-scaled intrinsic volumes and $k$-fac

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::d62aa14995ad0d17c3b078f1ef2ea9f5
https://doi.org/10.1007/s00440-014-0592-6

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Extreme values for characteristic radii of a Poisson-Voronoi Tessellation

Autor: Pierre Calka, Nicolas Chenavier

Publikováno v: Extremes. 17:359-385

A homogeneous Poisson-Voronoi tessellation of intensity $\gamma$ is observed in a convex body $W$. We associate to each cell of the tessellation two characteristic radii: the inradius, i.e. the radius of the largest ball centered at the nucleus and i

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3f311e7d4725e7e772adbf5ab9853a3a
https://doi.org/10.1007/s10687-014-0184-y

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