(3) 21:14 Lp-norm bounds for automorphic forms 57:43 Limitations to equidistribution in arithmetic progressions 27:53 Asymptotic mean square of product of higher derivatives of the zeta-function and 21:56 The generalised Shanks's conjecture 22:57 Logging of the zeta-function, but only for a ...
The asymptotic (3) is widely believed (it is a special case of the Chowla conjecture, which we will discuss in later notes; while there has been recent progress towards establishing it rigorously, it remains open for now. How would one try to make these probabilistic intuitions more rigorous...
The Central Limit Theorem (CLT) is a cornerstone of probability and statistics. The theorem states that as the sample size increases, the mean distribution among several samples will resemble a Normal Distribution. When you don't know how a data set is distributed, you can use the ...
just like a square is a two-dimensional shape (A^2); the constant factor of two here remains in the asymptotic ratio between the two, however, we ignore it like all factors... (
If we normalise the entries of the matrix to have mean zero and variance , then in the asymptotic limit , we have the Wigner semicircle law, which asserts that the eigenvalues are asymptotically distributed according to the semicircular distribution , where An essentially equivalent way of saying...
So how does something as small as photons act in such large numbers together to make a wavelength kilometres long? We still have many gaps in our knowledge which is not helped by learned people saying their guesswork is infallibly true so no need to bother working on this any more. ...
Presumably there is a sense in which two people could carry out this exercise, with only one of them “getting it right”, and the other “getting it wrong”. My question is what does “getting it right” mean to you? I’m not asking about particular inferential outputs, like point/int...
What does it mean for a rational function to be "proper"? What is a monoid in abstract algebra? What is the completeness of a relation? Which of the following sets of data represent valid functions? What are the applications of Galois representations? Is complex analysis used in statistics?
As such, for small, one can efficiently control the tail probabilities of in terms of the tail probability of a Poisson random variable of mean close to ; this is of course very closely related to the well known fact that the Poisson distribution emerges as the limit of sums of many indep...
More generally, the main result of our paper was that under the assumption that the predictor matrix obeys the RIP, the mean square error of the Dantzig selector is essentially equal to (2) and thus close to best possible. After accepting our paper, the Annals of Statistics took the (...