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math.CO/0602037: A correspondence principle between (hyper)graph theory and probability... - 0 views

front.math.ucdavis.edu/...0602037 correspondence-principle ergodic ergodicpnt graph transference
shared by arithwsun arithwsun on 31 Jul 07 - Cached
  • arithwsun arithwsun on 31 Jul 07
     
    The setting of this paper was deliberately placed at a midpoint between graph theory and ergodic theory, and the author hopes that it illuminates the analogies and interconnections between these two subjects.

Szemeredi's theorem - 30 views

started by arithwsun arithwsun on 03 Sep 07 no follow-up yet
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[math/0610021] The principle of the large sieve - 0 views

arxiv.org/0610021 e-print featured kowalski large-sieve
shared by arithwsun arithwsun on 23 Jul 08 - Cached
  • We describe a very general abstract form of sieve based on a large sieve inequality which generalizes both the classical sieve inequality of Montgomery (and its higher-dimensional variants), and our recent sieve for Frobenius over function fields. The general framework suggests new applications. We get some first results on the number of prime divisors of ``most'' elements of an elliptic divisibility sequence, and we develop in some detail ``probabilistic'' sieves for random walks on arithmetic groups, e.g., estimating the probability of finding a reducible characteristic polynomial at some step of a random walk on SL(n,Z). In addition to the sieve principle, the applications depend on bounds for a large sieve constant. To prove such bounds involves a variety of deep results, including Property (T) or expanding properties of Cayley graphs, and the Riemann Hypothesis over finite fields. It seems likely that this sieve can have further applications.
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A paper on the ArXiV « Gowers's Weblog - 0 views

gowers.wordpress.com/...a-paper-on-the-arxiv ergodicpnt gowers szemeredi
shared by arithwsun arithwsun on 17 Oct 07 - Cached
  • The paper itself is called “Hypergraph regularity and the multidimensional Szemerédi theorem.” At the bottom level, the basic idea of the paper is due to Ruzsa, Szemerédi and Rödl. Ruzsa and Szemerédi started the ball rolling with a short and very clever argument that showed that Szemerédi’s famous theorem on arithmetic progressions, in the case of progressions of length 3, could be deduced from Szemerédi’s almost as famous regularity lemma, a remarkable result that allows any graph to be partitioned into a bounded number of pieces, almost all of which “behave randomly.”
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Gowers' note for additive number theory - 0 views

www.dpmms.cam.ac.uk/...addnoth.notes.dvi additive-nt ergodicpnt expository featured fourier-analytic szemeredi vinogradov
shared by arithwsun arithwsun on 31 Jul 07 - No Cached
  • arithwsun arithwsun on 31 Jul 07
     
    I have proposed this course for the academic year 2006-7. The syllabus is Roth's theorem, the geometry of numbers, Freiman's theorem, quasirandomness of graphs and 3-uniform hypergraphs, and Szemerédi's regularity lemmaThe course will be examined as a 24
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Szemerédi's regularity lemma revisited - 0 views

arxiv.org/0504472 ergodicpnt information-theory probability-theory szemeredi
shared by arithwsun arithwsun on 31 Jul 07 - Cached
  • arithwsun arithwsun on 31 Jul 07
     
    one views the regularity lemma not as a structure theorem for large dense graphs, but rather as a structure theorem for events or random variables in a product probability space.
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Structure and randomness in combinatorics « What's new - 0 views

terrytao.wordpress.com/...nd-randomness-in-combinatorics combinatorics pseudorandom tao
shared by arithwsun arithwsun on 01 Aug 07 - Cached
  • arithwsun arithwsun on 01 Aug 07
     
    I've just uploaded to the arXiv my lecture notes "Structure and randomness in combinatorics" for my tutorial at the upcoming FOCS 2007 conference in October. This tutorial covers similar ground as my ICM paper (or slides), or my first two Simons lectures, but focuses more on the "nuts-and-bolts" of how structure theorems actually work to separate objects into structured pieces and pseudorandom pieces, for various definitions of "structured" and "pseudorandom".  Given that the target audience consists of computer scientists, I have focused exclusively here on the combinatorial aspects of this dichotomy (applied for instance to functions on the Hamming cube) rather than, say, the ergodic theory aspects (which are covered in Bryna Kra's lecture notes from Montreal, or my notes from Montreal for that matter).  While most of the known applications of these decompositions are number-theoretic (e.g. my theorem with Ben Green), the number theory aspects are not covered in detail in these notes.  (For that, you can read Bernard Host's Bourbaki article, Ben Green's http
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Harmonic Analysis on Finite Groups - Cambridge University Press - 0 views

www.cambridge.org/...catalogue.asp books
shared by arithwsun arithwsun on 01 Apr 08 - Cached
  • ContentsPart I. Preliminaries, Examples and Motivations: 1. Finite Markov chains; 2. Two basic examples on Abelian groups; Part II. Representation Theory and Gelfand Pairs: 3. Basic representation theory of finite groups; 4. Finite Gelfand pairs; 5. Distance regular graphs and the Hamming scheme; 6. The Johnson Scheme and the Laplace-Bernoulli diffusion model; 7. The ultrametric space; Part III. Advanced theory: 8. Posets and the q−analogs; 9. Complements on representation theory; 10. Basic representation theory of the symmetric group; 11. The Gelfand Pair (S2n, S2 o Sn) and random matchings; Appendix 1. The discrete trigonometric transforms; Appendix 2. Solutions of the exercises; Bibliography; Index.
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