The spectrum of some Poisson mosaic processes in the plane and the convex hull of the Brownian bridge

DOI10.1007/BF01192071zbMath0858.35094MaRDI QIDQ1917696

André Goldman

Publication date: 23 March 1997

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

zbMATH Keywords

Green's functionBrownian bridgepolygonal domainmosaic processspectral repartition function

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Brownian motion (60J65) Estimates of eigenvalues in context of PDEs (35P15) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

Related Items (12)

Asymptotic Methods for Random Tessellations ⋮ Boundedness of Crofton's cell for the homogeneous Poisson process of geodesics in the hyperbolic plane ⋮ The convex hull of the run-and-tumble particle in a plane ⋮ Convex hulls of random walks and their scaling limits ⋮ Mean perimeter and mean area of the convex hull over planar random walks ⋮ Empirical polygon simulation and central limit theorems for the homogeneous Poisson line process ⋮ Random convex hulls and extreme value statistics ⋮ Statistical and renewal results for the random sequential adsorption model applied to a unidirectional multicracking problem ⋮ Empirical (Typical) Cells of the Poisson Medial Tessellation ⋮ 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 ⋮ On a conjecture of D. G. Kendall concerning the planar Crofton cell and on its Brownian counterpart ⋮ The law of the smallest disk containing the typical Poisson-Voronoi cell

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