3
votes
1answer
129 views

Poisson point process (PPP) and Voronoi cells

Say we have a homogeneous PPP with rate $\lambda$ in the 2-D plane $\mathbb R^2$. In one realization of the PPP we get the points $\phi=\{x_1,x_2,...,x_i,...\}$. Now we generate the Voronoi cells ...
5
votes
1answer
149 views

Correlations between neighboring Voronoi cells

For a sequence $X_1,X_2,X_3,\ldots$ of random variables, what it means to say $X_1$ is correlated with $X_2$ is unambiguous. It may be that the bigger $X_1$ is, the bigger $X_2$ is likely to be. If, ...
3
votes
2answers
235 views

What is the average rotation angle needed to change the color of a sphere?

A sphere is painted in black and white. We are looking in the direction of the center of the sphere and see, in the direction of our vision, a point with a given color. When the sphere is rotated, at ...