Comments on: Additive combinatorics
http://terrytao.wordpress.com
Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence TaoThu, 24 Apr 2014 23:51:27 +0000hourly1http://wordpress.com/By: Anonymous
http://terrytao.wordpress.com/books/additive-combinatorics/#comment-277849
Sun, 23 Mar 2014 14:55:33 +0000http://terrytao.wordpress.com/books/additive-combinatorics/#comment-277849can any one please explain me the concept of “uniformly chosen random subset of a unit interval of cardinality N”.??
]]>By: Metric entropy analogues of sum set theory | What's new
http://terrytao.wordpress.com/books/additive-combinatorics/#comment-277056
Thu, 20 Mar 2014 01:30:19 +0000http://terrytao.wordpress.com/books/additive-combinatorics/#comment-277056[…] estimates (which are covered, incidentally, in Section 2 of my book with Van Vu) are particularly useful for controlling finite sets of small doubling, in the sense that for […]
]]>By: Szemerédi’s Theorem Part I – Equivalent formulations | I Can't Believe It's Not Random!
http://terrytao.wordpress.com/books/additive-combinatorics/#comment-269870
Wed, 05 Feb 2014 03:01:12 +0000http://terrytao.wordpress.com/books/additive-combinatorics/#comment-269870[…] Szemerédi used a complicated combinatorial argument. Two years later Furstenberg provided a different proof of this result, using ergodic theory and a correspondence principle which allows one to derive conclusions about sets of integers by studying dynamics on certain measure spaces. It should also be mentioned that a third proof of the Szemerédi’s Theorem was discovered by Gowers in 2001, generalizing Roth’s harmonic analysis proof of the existence of progressions of length in a set of positive density, to progressions of arbitrary length and having the advantage of providing concrete bounds for the finitistic version. More recently a number of different proofs appeared. A good discussion on the different proofs and similarities between them can be found on chapters 10 and 11 of the Tao and Vu’s book. […]
]]>By: Real stable polynomials and the Kadison-Singer problem | What's new
http://terrytao.wordpress.com/books/additive-combinatorics/#comment-249983
Mon, 04 Nov 2013 21:48:52 +0000http://terrytao.wordpress.com/books/additive-combinatorics/#comment-249983[…] as the second moment method, exponential moment method, and zeroth moment method, see Chapter 1 of my book with Van Vu. For a general discussion of the probabilistic method, see the book by Alon and Spencer of the same […]
]]>By: Rex
http://terrytao.wordpress.com/books/additive-combinatorics/#comment-239113
Fri, 19 Jul 2013 10:12:21 +0000http://terrytao.wordpress.com/books/additive-combinatorics/#comment-239113Oh, nevermind. My mistake
]]>By: Rex
http://terrytao.wordpress.com/books/additive-combinatorics/#comment-239112
Fri, 19 Jul 2013 10:10:23 +0000http://terrytao.wordpress.com/books/additive-combinatorics/#comment-239112p. 14: In the last display, the first sign should be . (just as with pg. 15)
]]>By: Rex
http://terrytao.wordpress.com/books/additive-combinatorics/#comment-239042
Thu, 18 Jul 2013 17:51:44 +0000http://terrytao.wordpress.com/books/additive-combinatorics/#comment-239042Just so you know, the .dvi file on entropy sumset methods has some formulas that run completely off the page (so they are not visible)
]]>By: Rex
http://terrytao.wordpress.com/books/additive-combinatorics/#comment-238922
Wed, 17 Jul 2013 14:32:25 +0000http://terrytao.wordpress.com/books/additive-combinatorics/#comment-238922On page 4: “Theorem 1.3 was proved by Erdos in 1965 [86]. Several years later, Bourgain [37] used harmonic analysis arguments to improve the bound slightly.”

It seems that a better description might be: “Three decades later, Bourgain used….”

]]>By: Tomer Shalev
http://terrytao.wordpress.com/books/additive-combinatorics/#comment-233198
Fri, 07 Jun 2013 10:49:35 +0000http://terrytao.wordpress.com/books/additive-combinatorics/#comment-233198page 163: after “(for instance)” if we set A = Z … ||z||_u should be zero, but instead, what is written is ||B||_u = tao*Z + O(…) , (tao*Z should be canceled I believe).

[Corrected, thanks - T.]

]]>By: Jarek Kuben
http://terrytao.wordpress.com/books/additive-combinatorics/#comment-219634
Sun, 17 Mar 2013 01:28:31 +0000http://terrytao.wordpress.com/books/additive-combinatorics/#comment-219634In the proof of Theorem 9.2, page 331, 15th line, should be t_{n-1}^{d_{n-1}} instead of t_{n-1}^{d_{n}-1}.