Publications de Pierre Calka

 

Thèmes de recherche

   Probabilité, géométrie aléatoire et en particulier

  • mosaïques aléatoires,
  • ensembles convexes et polytopes aléatoires,
  • modèle booléen et recouvrements aléatoires.

Articles

  • Elongated Poisson-Voronoi cells in an empty half-plane. Pierre Calka, Yann Demichel & Nathanaël Enriquez, 2022. [HAL]
  • Convex hulls of perturbed random point sets. Pierre Calka & J. E. Yukich. Ann. Appl. Probab. 31 2021, p. 1598-1632. [HAL]
  • Poisson-Voronoi tessellation on a Riemannian manifold. Pierre Calka, Aurélie Chapron & Nathanaël Enriquez. Int. Math. Res. Not. 2021 2021, p. 5413-5459. Full version `Mean asymptotics for a Poisson-Voronoi cell on a Riemannian manifold' available at [HAL]
  • Large planar Poisson-Voronoi cells containing a given convex body. Pierre Calka, Yann Demichel & Nathanaël Enriquez. Ann. H. Lebesgue 4 2021, p. 711-757. Full version `The Poisson-Voronoi cell around an isolated nucleus' available at [HAL]
  • Cells with many facets in a Poisson hyperplane tessellation. Gilles Bonnet, Pierre Calka & Matthias Reitzner. Adv. Math. 324 2018, p. 203-240. [HAL]
  • Variance asymptotics and scaling limits for random polytopes. Pierre Calka & J. E. Yukich. Adv. Math. 304 2017, p. 1-55. [HAL]
  • Variance asymptotics and scaling limits for Gaussian polytopes. Pierre Calka & J. E. Yukich. Probab. Theory Related Fields. 163 (1) 2015. p. 259-301. [HAL]
  • Fractal random series generated by Poisson-Voronoi tessellations. Pierre Calka & Yann Demichel. Trans. Amer. Math. Soc. 367 2015. p. 4157-4182. [HAL]
  • Extreme values for characteristic radii of a Poisson-Voronoi tessellation. Pierre Calka & Nicolas Chenavier. Extremes. 17 2014. p. 359-385. [HAL]
  • Variance asymptotics for random polytopes in smooth convex bodies. Pierre Calka & J. E. Yukich. Probab. Theory Related Fields. 158 (1-2) 2014. p. 435-463. [HAL]
  • Asymptotics of visibility in the hyperbolic plane. Johan Tykesson & Pierre Calka. Adv. in Appl. Probab. 45 (2) 2013. p. 332-350. [HAL]
  • Brownian limits, local limits and variance asymptotics for convex hulls in the unit ball. Pierre Calka, Tomasz Schreiber & J. E. Yukich. Ann. Probab. 41 (1) 2013. p. 50-108. [HAL]
  • Refined convergence for the Boolean model. Pierre Calka, Julien Michel & Katy Paroux. Adv. in Appl. Probab. 41 (4) 2009. p. 940-957. [HAL]
  • Visibilité dans le modèle booléen (preliminary note). Pierre Calka, Julien Michel & Sylvain Porret-Blanc. Comptes-Rendus Mathématique 347 (11-12) 2009. p. 659-662. [PDF]
  • Sylvester's question and the Random Acceleration Process. Henk Hilhorst, Pierre Calka & Grégory Schehr. J. Stat. Mech. P10010 2008. P10010 [arxiv]
  • Random line tessellations of the plane: statistical properties of many-sided cells. Henk Hilhorst & Pierre Calka. J. Stat. Phys. 132 (4) 2008. p. 627-647. [arxiv]
  • Large deviation probabilities for the number of vertices of random polytopes in the ball. Pierre Calka & Tomasz Schreiber. Adv. in Appl. Probab. 38 (1) 2006. p. 47-58. [PDF]
  • Limit theorems for the typical Poisson-Voronoi cell and the Crofton cell with a large inradius. Pierre Calka & Tomasz Schreiber. Ann. Probab. 33 (4) 2005. p. 1625-1642. [PDF]
  • Statistical and renewal results for the random sequential adsorption model applied to a unidirectional multicracking problem. Pierre Calka, André Mézin & Pierre Vallois. Stoch. Proc. Appl. 115 (6) 2005. p. 983-1016. [PDF]
  • On the spectral function of the Poisson-Voronoi cells. André Goldman & Pierre Calka. Ann. Inst. H. Poincaré Probab. Statist. 39 (6) 2003. p. 1057-1082. [PDF]
  • An explicit expression of the distribution of the number of sides of the typical Poisson-Voronoi cell . Pierre Calka. Adv. in Appl. Probab. 35 (4) 2003. p. 863-870. [PDF]
  • Precise formulae for the distributions of the principal geometric characteristics of the typical cells of a two-dimensional Poisson-Voronoi tessellation and a Poisson line process. Pierre Calka. Adv. in Appl. Probab. 35 (3) 2003. p. 551-562. [PDF]
  • The distributions of the smallest disks containing the Poisson-Voronoi typical cell and the Crofton cell in the plane. Pierre Calka. Adv. in Appl. Probab. 34 (4) 2002. p. 702-717. [PDF]
  • La loi du plus petit disque contenant la cellule typique de Poisson-Voronoi. Pierre Calka. C. R. Acad. Sci. Paris, Série I Math. 334 (4) 2002. p. 325-330.
  • Sur la fonction spectrale des cellules de Poisson-Voronoi. André Goldman & Pierre Calka. C. R. Acad. Sci. Paris, Série I Math. 332 (9) 2001. p. 835-840.
  • Mosaïques poissoniennes de l'espace euclidien. Une extension d'un résultat de R. E. Miles. Pierre Calka. C. R. Acad. Sci. Paris, Série I Math. 332 (6) 2001. p. 557-562.

Chapitres de livres

  • Mosaïque de Poisson-Voronoi sur une surface. Pierre Calka, Aurélie Chapron et Nathanaël Enriquez. Contributed chapter of Séminaire de Probabilités L, edited by Catherine Donati-Martin, Antoine Lejay et Alain Rouault, Lecture Notes in Math. 2252, Springer, Cham 2019.
  • Some classical problems in random geometry. Pierre Calka. Contributed chapter of Stochastic Geometry, edited by David Coupier, Lecture Notes in Math. 2237, Springer, Cham 2019. [HAL]
  • Asymptotic properties of random polytopes. Pierre Calka. Contributed chapter of Geometric science of information, edited by Frank Nielsen et al., Lecture Notes in Computer Science 9389, Springer, Cham 2015.
  • Asymptotic methods for random tessellations. Pierre Calka. Contributed chapter of Lectures on Stochastic Geometry, Spatial Statistics and Random Fields edited by Evgeny Spodarev, Lecture Notes in Math. 2068, Springer, Cham 2012. [PDF]
  • Tessellations. Pierre Calka. Contributed chapter of New Perspectives in Stochastic Geometry edited by W. S. Kendall and I. Molchanov, Oxford University Press 2010. [PDF]

Habilitation et thèse

  • Mosaïques, enveloppes convexes et modèle Booléen : quelques propriétés et rapprochements. Pierre Calka. Document de synthèse en vue de l'obtention de l'habilitation à diriger des recherches, soutenue le 10 décembre 2009. [TEL]
  • De nouveaux résultats sur la géométrie des mosaïques de Poisson-Voronoi et des mosaïques poissoniennes d'hyperplans. Etude du modèle de fissuration de Rényi-Widom. Pierre Calka. Thèse soutenue le 5 décembre 2002 à l'université Lyon 1, sous la direction de André Goldman. [TEL]

Manuscrits non publiés

  • Asymptotics of the visibility function in the Boolean model. Pierre Calka, Julien Michel & Sylvain Porret-Blanc. 2010. [PDF]
  • Poissonian tessellations of the Euclidean space. An extension of a result of R. E. Miles . Pierre Calka. 2003. [PDF]
  • A rigorous proof of a result of R. E. Miles concerning the thickened Poisson hyperplane process in Rd. Pierre Calka. 2002.
Mise à jour le 23/03/2022