Hausdorff dimension of the SLE curve intersected with the real line.
How many intervals cover a point in random dyadic covering?
How To Build a Barricade.
Improved inclusion-exclusion inequalities for simplex and orthant arrangements.
Integration in a dynamical stochastic geometric framework
Motivated by the well-posedness of birth-and-growth processes, a stochastic geometric differential equation and, hence, a stochastic geometric dynamical system are proposed. In fact, a birth-and-growth process can be rigorously modeled as a suitable combination, involving the Minkowski sum and the Aumann integral, of two very general set-valued processes representing nucleation and growth dynamics, respectively. The simplicity of the proposed geometric approach allows to avoid problems of boundary...
Integration in a dynamical stochastic geometric framework
Motivated by the well-posedness of birth-and-growth processes, a stochastic geometric differential equation and, hence, a stochastic geometric dynamical system are proposed. In fact, a birth-and-growth process can be rigorously modeled as a suitable combination, involving the Minkowski sum and the Aumann integral, of two very general set-valued processes representing nucleation and growth dynamics, respectively. The simplicity of the proposed geometric approach allows to avoid problems of boundary...
Interpolation of random hyperplanes.
Intrinsic volumes and f-vectors of random polytopes.
Isomorphically isometric probabilistic normed linear spaces.
Probabilistic normed linear spaces (briefly PNL spaces) were first studied by A. N. Serstnev in [1]. His definition was motivated by the definition of probabilistic metric spaces (PM spaces) which were introduced by K. Menger and subsequebtly developed by A. Wald, B. Schweizer, A. Sklar and others.In a previuos paper [2] we studied the relationship between two important classes of PM spaces, namely E-spaces and pseudo-metrically generated PM spaces. We showed that a PM space is pseudo-metrically...
Iterated Boolean random varieties and application to fracture statistics models
Models of random sets and of point processes are introduced to simulate some specific clustering of points, namely on random lines in and and on random planes in . The corresponding point processes are special cases of Cox processes. The generating distribution function of the probability distribution of the number of points in a convex set and the Choquet capacity are given. A possible application is to model point defects in materials with some degree of alignment. Theoretical results...
Iterations of translative integral formulae and non-isotropic Poisson processes of particles.
L'aiguille de Buffon sur la sphère.
Laslett’s transform for the Boolean model in
Consider a stationary Boolean model with convex grains in and let any exposed lower tangent point of be shifted towards the hyperplane by the length of the part of the segment between the point and its projection onto the covered by . The resulting point process in the halfspace (the Laslett’s transform of ) is known to be stationary Poisson and of the same intensity as the original Boolean model. This result was first formulated for the planar Boolean model (see N. Cressie [Cressie])...
Les notions de probabilite dans quelques reflexions de Bošković dans sa theorie de la philosophie naturelle
L'estimation du spectre de processus de droites
L'exponentielle stochastique des groupes de Lie
Limit theorems for geometric functionals of Gibbs point processes
Observations are made on a point process in in a window of volume . The observation, or ‘score’ at a point , here denoted , is a function of the points within a random distance of . When the input is a Poisson or binomial point process, the large limit theory for the total score , when properly scaled and centered, is well understood. In this paper we establish general laws of large numbers, variance asymptotics, and central limit theorems for the total score for Gibbsian input ....
Limit theorems for the number of maxima in random samples from planar regions.
Limsup random fractals.
Martingale representation and a simple proof of logarithmic Sobolev inequalities on path spaces.