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Results tagged with geometric-probability
Search options questions only
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user 70190
4
votes
1
answer
116
views
Distribution of the $pn$ shortest edges out of $n$ uniform points, $p\to 0$
Suppose I sample $n$ points independently and uniformly at random in the unit square, and then I select the $pn$ shortest edges between all pairs of points, for fixed $0<p<1$. For large $n$ and small …
- 4,049
4
votes
1
answer
2k
views
What is the nearest-neighbor distribution in this picture?
Consider the following process: sample $n$ points uniformly at random in the unit square, and for each point $i$, let $d_i$ be the distance from $i$ to its nearest neighbor. Finally, let $z_i = d_i\ …
- 4,049
8
votes
2
answers
256
views
What is the probability that these sets intersect?
Let $A$ be the subset of $\mathbb{R}^n$ defined by $A=\{x\in\mathbb{R}^{n}:|x_{1}-x_{n}|+\sum_{i=1}^{n-1}|x_{i+1}-x_{i}|\leq d\}$ for a given $d$. Next, sample a point $p$ uniformly in the unit cube, …
- 4,049
2
votes
0
answers
63
views
Limiting distribution of separated points in a unit square
Let $n$ and $r$ be fixed, and consider the following process, with $S=\emptyset$ to start:
For $i\in\{1,\dots,n\}$:
Sample a random point $X$ in the unit square.
If $X$ is a distance at least $r$ fr …
- 4,049