A Clt concerning Critical Points of Random Functions on a Euclidean Space

On images of continuous functions from a compact manifold to Euclidean space

Statistics of Linear Families of Smooth Functions on Knots

Given a knot K in an Euclidean space R, and a finite dimensional subspace V ⊂ C∞(K), we express the expected number of critical points of a random function in V in terms of an integral-geometric invariant of K and V . When V consists of the restrictions to K of homogeneous polynomials of degree ` on R, this invariant takes the form of total curvature of a certain immersion of K. In particular, ...

Umbilicity of (Space-Like) Submanifolds of Pseudo-Riemannian Space Forms

We study umbilic (space-like) submanifolds of pseudo-Riemannian space forms, then define totally semi-umbilic space-like submanifold of pseudo Euclidean space and relate this notion to umbilicity. Finally we give characterization of total semi-umbilicity for space-like submanifolds contained in pseudo sphere or pseudo hyperbolic space or the light cone.A pseudo-Riemannian submanifold M in (a...

On Poisson and Composed Poisson Stochastic Set Functions

Several investigations has recently been made concerning Poisson and composed Poisson stochastic processes. The ordinary Poisson process is conceivable as a sequence of points, distributed at random on the time axis and this idea can be generalized to more than onedimensional spaces. The latter case occurs in making a blood-count, in counting stars, etc. In [8], [4], [6] and [15] conditions are...

Clt S for Poisson Hyperplane Tessellations

We derive a central limit theorem for the number of vertices of convex polytopes induced by stationary Poisson hyperplane processes in R d. This result generalizes an earlier one proved by Paroux [Adv. for intersection points of motion-invariant Poisson line processes in R 2. Our proof is based on Hoeffd-ing's decomposition of U-statistics which seems to be more efficient and adequate to tackle...