All Questions
Tagged with topological-groups pr.probability
7 questions
11
votes
0
answers
263
views
Which results in probabilistic group theory generalize from finite groups to compact Hausdorff groups (and which don't)?
Let $G$ be a finite group. It has been shown that:
If the probability that two randomly selected elements of $G$ generate an abelian group is greater than $5/8$, $G$ is abelian.
If the probability ...
- 495
67
votes
1
answer
7k
views
Why can't a nonabelian group be 75% abelian?
This question asks for intuition, not a proof.
An earlier question,
Measures of non-abelian-ness
was thoroughly answered by Arturo Magidin.
A paper by Gustafson1
proves that, for a nonabelian group,
...
- 47.3k
3
votes
2
answers
278
views
The disintegration of the convolution of two probability measures
Let $G$ be a topological group with all the topological conditions in order that some form of the disintegration theorem be applicable (for instance, take $G$ metrizable). Let $N$ be normal and closed,...
CommunityBot
- 1
3
votes
1
answer
167
views
When are all the convolution roots of an infinitely divisible probability measure infinitely divisible?
Let $G$ be a topological group.
Let us say that a probability measure $\mu$ on $G$ is strongly infinitely divisible (SID) if $\mu$ is infinitely divisible and any probability measure $\nu$ on $G$ ...
- 91.8k
2
votes
0
answers
80
views
Are the roots of an infinitely divisible probability infinitely divisible themselves?
Let $\mu$ be an infinitely divisible probability on a topological group $G$. If $\nu ^{* n} = \mu$ for some $n$, is $\nu$ an infinitely divisible probability too?
A sufficient criterion would be to ...
CommunityBot
- 1
4
votes
2
answers
359
views
Random walk uniformly hitting a compact set
Suppose $G$ is a locally compact compactly generated group. Let $\mu$ be a probability measure that is:
Adapted to $G$, i.e. there is no proper subgroup $H$ such that $\mu(H)=1$.
Symmetric, i.e. $\...
- 128k
1
vote
2
answers
635
views
Mean value theorems for the Haar integral?
Let $G$ be a compact topological group (feel free to add hypotheses if necessary). Is there any mean value theorem for its (normalized to 1) Haar integral?
In general, are there mean value theorems ...
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