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Results tagged with pr.probability
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user 28104
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
21
votes
When has the Borel-Cantelli heuristic been wrong?
The Borel-Cantelli heuristic suggests that for any odd $n \in \mathbb{N}$, there is some
$k \in \mathbb{N}$ such that $n+2^k$ is prime -- and for small $n$ this is in fact true
(in particular, for any …
- 19.6k
2
votes
Accepted
Dixon's Theorem
If you have two elements of ${\rm A}_n$ which do not lie both in any maximal subgroup of
${\rm A}_n$, then they in particular do not lie both in any proper subgroup of ${\rm A}_n$.
This in turn means …
- 19.6k
9
votes
Probability that randomly chosen integers from a restricted set of natural numbers are coprime
First of all, note that there is no canonical notion of equidistribution on a countable set
like the integers.
When asking for the probability that $k$ 'randomly chosen' integers are coprime,
it is m …
- 19.6k