All Questions
5 questions
4
votes
1
answer
243
views
Does there exist a scale invariant random packing of circles in the plane?
I want to construct a scale invariant random packing of the plane with circles.
Here is a way to construct a rotationally invariant, but not scale invariant random packing of the plane with circles:
...
- 1,054
-1
votes
1
answer
96
views
On bounding a certain discrepancy between probability distributions on the symmetric group
Disclaimer. This is a follow up to a question I asked and answered on SE https://math.stackexchange.com/q/3579311/168758. The question was about upper-bounds. Here I'm interested in lower bounds, and ...
- 6,853
3
votes
1
answer
473
views
On 4 random points in a rectangle [closed]
Given a bounded rectangular area, I generate 4 random points. What is the probability that the fourth point lie within a triangle formed the first 3?
How would I attack this problem? The goal is to ...
- 133
5
votes
1
answer
460
views
The expectation of two sides of rectangle is equal. Can we deduce that in the expectation the rectangle is not very far from being a square?
Let $T$ be a set of $n\ge 3$ points in the plane such that not all of them lie in a common line. Pick two distinct points $\{a=\left( \begin{array}{c} a_{1} \\a_{2} \end{array} \right) ,b=\left( \...
- 519
6
votes
3
answers
298
views
Probability of random geodesics on the half-sphere intersecting
4 end points (a,b,c,d say) are chosen uniformly randomly and connected a to b and c to d by two geodesics on the 2-dim half-sphere. Here, uniform means that, probability that a point lies on a surface ...
