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Results tagged with gr.group-theory
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user 1004
Questions about the branch of algebra that deals with groups.
6
votes
Accepted
Fundamental group of punctured simply connected subset of $\mathbb{R}^2$
Here is a proof that $\pi_1(S\setminus\{x\})\cong\mathbb Z$. It is along similar lines to Jeremy Brazas' answer, and also makes use of Lemma 13 from the paper The fundamental groups of subsets of clos …
- 17.1k
13
votes
Accepted
What is a Gaussian measure?
You could alternatively try defining Gaussian measures as $2$-stable distributions. This does remove any reliance on finite dimensional projections, and even removes reference to topology. Let $V$ be …
- 17.1k
8
votes
Accepted
Random Walks in $Z^2$/$Z^2$-intrinsic characterization of Euclidean distance Part II
As I mentioned in my comment - what you are suggesting implies that the probability of being at (3,4) is the same as being at (5,0) for all large $n$. That seems unlikely, and would guess that $C_n=5$ …
- 17.1k
6
votes
Accepted
Symmetric groups and Poisson processes
This isn't a problem I've looked at before, but I've been thinking about it since reading your post, and there does seem to be an interesting limit. The following looks like it should all work out, bu …
- 17.1k