Follow–up to "Modern algebra and the Poisson point process".

Follow-up to Modern algebra and the Poisson point process from Random Curiosities

Here is a related question. Suppose I show you a network of intersecting lines, and I secretly choose a self-avoiding path on the line network. I tell you the total lengths of the intersections of this self-avoiding path with each line on the network. Can you then reconstruct the path?

For networks of lines in general position, the answer is "yes", using an argument based on the ideas in the "Modern algebra and the Poisson point process" post.

However this is not the case for all networks, and in particular it is not the case for a network determining a regular cartesian grid. Ed Kendall demonstrated this by exhibiting the following counterexample.

Wilfrid Kendall : 12 Mar 2022 12:06 |  Comments (0) |  Report a problem