Comments on: Soft analysis, hard analysis, and the finite convergence principle
https://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/
Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence TaoThu, 27 Oct 2016 03:18:46 +0000hourly1http://wordpress.com/By: The logarithmically averaged Chowla and Elliott conjectures for two-point correlations; the Erdos discrepancy problem | What's new
https://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-459432
Sat, 19 Sep 2015 00:46:38 +0000http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-459432[…] at some point one must reach a metastable region (cf. the finite convergence principle discussed in this previous blog post), within which very little mutual information can be shared between the sequence and the graph . […]
]]>By: O intâlnire cu informatica teoretică românească: FMI@150 Ziua I | Isarlâk
https://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-243296
Fri, 30 Aug 2013 20:20:36 +0000http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-243296[…] de faptul că domeniul este unul interesant vă puteți convinge de exemplu citind această discuție pe blogul lui Terry Tao. Ar fi interesant de văzut câte din lucrurile din acest domeniu pot fi automatizate. Impresia pe […]
]]>By: Topological order for mixed states | Tobias J. Osborne's research notes
https://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-231779
Wed, 29 May 2013 20:40:28 +0000http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-231779[…] The definition provided by Hastings is much closer in spirit with this second definition. (It’s worth noting that by working in the infinite lattice size limit we can avoid lots of s and s; we can make our soft analysis definition a hard analysis definition if we like in the standard way.) […]
]]>By: Analogies between finitary and infinitary math | Abstract Art
https://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-230426
Mon, 20 May 2013 15:04:02 +0000http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-230426[…] [1.3] Soft analysis, hard analysis, and the finite convergence principle […]
]]>By: Frank
https://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-230111
Sat, 18 May 2013 05:28:15 +0000http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-230111Dear professor:
Sorry for my ignorance. In my opinion, the proof of the part (the infinite convergence principle implying the finite convergence principle) is imperfect. The compactness or completeness of the real line might as well be avoided, since the theorem, i.e, the monotone sequence of rational numbers on is Cauchy as well. The compactness of depends on that, I think.
]]>By: andrescaicedo
https://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-230025
Fri, 17 May 2013 19:50:42 +0000http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-230025Jennifer Chayes’s link is outdated. The current link should be http://research.microsoft.com/en-us/um/people/jchayes/

[Corrected, thanks – T.]

]]>By: Bird’s-eye views of Structure and Randomness (Series) | Abstract Art
https://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-228784
Sat, 11 May 2013 06:05:12 +0000http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-228784[…] Analogies between finitary and infinitary math (adapted from “Soft analysis, hard analysis and the finite convergence principle“) […]
]]>By: The spectral proof of the Szemeredi regularity lemma « What’s new
https://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-199142
Tue, 04 Dec 2012 01:35:50 +0000http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-199142[…] with for all . Applying (3) and the pigeonhole principle (or the finite convergence principle, see this blog post), we can find such […]
]]>By: The three Moirai, continued « chorasimilarity
https://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-195459
Fri, 23 Nov 2012 11:57:30 +0000http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-195459[…] Now the construction is finished, let us let the Moirai to do their job. Finally, I shall recall my real goal, which I have never forgot. The real goal is to pass from understanding of the power of this lambda calculus sector of graphic lambda calculus to the real deal, called “computing with space”, namely to understand space from a computational perspective, not as a given receptacle, but as a small list of procedures along with some impossible to verify assertions (like that we may rescale indefinitely space), see “emergent algebras”, which can always be eliminated a posteriori, by a kind of finitization procedure. […]
]]>By: Walsh’s ergodic theorem, metastability, and external Cauchy convergence « What’s new
https://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-185892
Thu, 25 Oct 2012 18:10:45 +0000http://terrytao.wordpress.com/2007/05/23/soft-analysis-hard-analysis-and-the-finite-convergence-principle/#comment-185892[…] which is useful in situations in which one does not expect a uniform convergence rate; see this previous blog post for some discussion of metastability. When interpreted in a finitary setting, this concept requires […]
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