“The parity problem can also be sometimes be overcome when there is an exceptional Siegel zero … [this] suggests that to break the parity barrier, we may assume without loss of generality that there are no Siegel zeroes.” On the other hand, it was pointed out in a more recent articl...
This result has a number of applications, for instance to establishing asymptotics for linear equations in the primes, but this will not be the focus of discussion here. The purpose of this post is to record the observation that this “discrete” inverse theorem, together with an ...
Really I'm trying to lay out the options, not draw any profound conclusion from all this. But as you may have already guessed, there does not seem to be any option that offers 1:1 parity with all of the different material systems available. Certainly a "monolithic" extension could include...
P is the probability of a shard failing at least once in R days D is the durability of data over R days: not too many shards are lost With erasure coding, your data remains intact as long as you don’t lose more shards than there are parity shards. If you do lose more, there is...
Why is there an arrow of time? What is the nature of time? What physics lies at the heart of the mathematical singularities incapable of penetrating reality any further? What happened at (or even before) the Big Bang? Is our universe infinite or finite in extent?
(Forum of Mathematics, Sigma) which is in turn loosely organised for editorial purposes into “clusters” for each of the major subfields of mathematics (analysis, topology, algebra, discrete mathematics, etc.). As a first approximation, Pi is intended as a top-tier journal (on the level of...
of that homomorphism; and furthermore, one should only be close to equality if the fibers “line up” in some sense. Here is the fibring identity: Proposition 5 (Fibring identity)Let be a homomorphism. Then for any independent -valued random variables ...
14 February, 2013 in expository, math.AP | Tags: conformal symmetry, pseudoconformal symmetry, Schrodinger equation, wave equation | by Terence Tao | 7 comments Consider the free Schrödinger equation in spatial dimensions, which I will normalise as where is the unknown field and is the spa...
10 November, 2009 inexpository,Logic reading seminar,math.CO| Tags:Freiman's theorem| byTerence Tao|16 comments Let be a finite subset of a non-commutative group . As mentionedpreviously on this blog(as well as in the currentlogic reading seminar), there is some interest in classifying thos...
The influence can range between 0 (for constant functions +1, -1) and n (for the parity function or its negation). If f has mean zero (i.e. it is equal to +1 half of the time), then the edge-isoperimetric inequality asserts that (with equality if and only if there is a ...