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Results tagged with reference-request
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user 29697
This tag is used if a reference is needed in a paper or textbook on a specific result.
30
votes
1
answer
2k
views
How strong is this conjecture? $(Z/nZ)^*$ is generated by "small" elements
Conjecture: There are constants $c,k$ such that every $(Z/nZ)^*$ is generated by its elements smaller than $k (\log n)^c$.
Where $(Z/nZ)^*$ is the multiplicative group of integers mod $n$. My mai …
- 4,529
22
votes
Accepted
information-theoretic derivation of the prime number theorem
You may be interested in this arxiv paper [1], "Some information-theoretic computations related to the distribution of prime numbers", Ioannis Kontoyiannis, 2007.
It discusses Chebyshev's 1852 result, …
- 4,529
4
votes
1
answer
472
views
Concentration inequalities in $\ell_{\infty}$ for sums of iid random ("nice") functions?
I'm looking for "tail-bound-like" inequalities that look like this (I state a specific setting but more general settings are interesting):
Let $D$ be a distribution on a set of "nice" functions $g …
- 4,529
4
votes
Proofs of main probability results from other fields
Maybe this is a stretch, but laws of large numbers, and more precise concentration of measure bounds, can be proven by the "isoperimetric" approach which can be called geometric and was pioneered by T …
4
votes
2
answers
697
views
Existence of a strictly convex function interpolating given gradients and values
I'm wondering where to find a proof and reference for the following facts, which I feel sure must be true.
(1) Suppose we are given a finite set of points in $\mathbb{R}^{d+1}$. For each point, we ar …
- 4,529
3
votes
Can we do better than Azuma-Hoeffding when the variance is small?
Adding to Iosif Pinelis' answer, there are two points here. First, as he says, the fact that we have a martingale rather than i.i.d. variables doesn't change much as proofs generally extend. So, secon …
- 4,529
3
votes
Accepted
Should mixed strategies in normal form games be interpreted as measurable functions or proba...
This could be a comment but it might clear things up. In short, a mixed strategy is a probability measure over a set of pure strategies (also called actions). If the set of actions is finite, we can r …
- 4,529
1
vote
Looking for a certain kind of a distribution
In general, you are just asking about a weighted sum of i.i.d. variables from distribution $D$, with weights $\alpha_1,\dots,\alpha_n$. The Gaussian distribution is the only one that is rotationally i …
- 4,529
0
votes
Reference Request: Representing Positive Integers as Differences with Minimal Hamming Weight
More extended comment than answer:
My understanding is that this is basically the idea behind the Fast Fourier transform multiplication algorithm. My impression is that the intuition behind finding F …
- 4,529