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Results tagged with intuition
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user 4600
Questions asking for the intuition behind some definition, conjecture, proof etc. In other words, questions designed to improve or to acquire understanding on a conceptual or intuitive level, as opposed to on a technical or formal level. When asking such a question it can be helpful to include a rough description of ones understanding of the subject at hand (on a technical level).
8
votes
How to explain the concentration-of-measure phenomenon intuitively?
If
$$x_1^2+\dots+x_{n+1}^2=1$$
then
$$
x_1^2+\dots+x_n^2 = 1-x_{n+1}^2 \in [0,1].
$$
Now $S = \sum_{i=1}^n x_i^2$ for $-1\le x_i\le 1$ has expectation $c\cdot n$ for a certain $c>0$, and will be appro …
- 24.8k
6
votes
Intuition and/or visualisation of Itô integral/Itô's lemma
One way to improve intuition is to work out a couple of
Discrete versions of Ito's lemma
Øksendal (6th edition) Example 3.1.9: almost surely,
$$
B_t^2 - t = \int_0^t 2B_s dB_s
$$
This has …
- 24.8k
4
votes
Can we define an "empirically generic" real number?
It sounds like you are talking about what in computability theory and set theory are known as Cohen generic reals (the lowest level of which in computability theory is 1-generic, then 2-generic and so …
- 24.8k
17
votes
Intuition of law of iterated logarithm?
One nice fact that helps intuition is that
the $\log\log n$ factor "disappears on a sparse subsequence". …
- 24.8k