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20 votes
5 answers
1k views

Iterated Circumcircle

Take three noncollinear points (a,b,c), compute the center of their circumcircle x, and replace a random one of a,b,c with x. Repeat. It seems this process may converge to a point, assuming no ...
Joseph O'Rourke's user avatar
17 votes
2 answers
2k views

Random walk is to diffusion as self-avoiding random walk is to ...?

One can view a random walk as a discrete process whose continuous analog is diffusion. For example, discretizing the heat diffusion equation (in both time and space) leads to random walks. Is there a ...
Joseph O'Rourke's user avatar
16 votes
3 answers
2k views

A random walk on random lines

I am wondering if this random walk remains finite with positive probability. Start with three lines $A,B,C$ that are extensions of an equilateral triangle. Let $p_0$ be one corner. Generate a line $...
Joseph O'Rourke's user avatar
2 votes
0 answers
71 views

Reference request- Automorphisms of point processes

A suspension of a point process on $\mathbb{R}^d$ is a measure preserving automorphism of the (distribution of the) point process which is determined by a map $T:\mathbb{R}^d\to\mathbb{R}^d$. The ...
user103342's user avatar