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13 votes

The metric of the expected difference of random variables

Before this question gets closed (although I don't see any reason for that), I would like to point out that although this metric looks like the $L^1$ norm, it actually is not (the OP tried to point th …
R W's user avatar
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2 votes
Accepted

Union of random half spaces cover a ray

You should look instead at the probability $p_m$ that $$ y\notin \bigcup_{i=1}^m \mathcal H(a_i) \;, $$ or, in other words, that $\langle y, a_i \rangle < 0$ for all $a_i$. Since $a_i$ are independen …
R W's user avatar
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1 vote
Accepted

On bounding a certain discrepancy between probability distributions on the symmetric group

There is no non-trivial lower bound as it is well possible that $P\neq Q$, whereas $p_{ij}=q_{ij}$ for all pairs of $i$ and $j$. The reason is that (as you point out), these numbers are nothing but th …
R W's user avatar
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