Comments on: 254B, Notes 3: Quasirandom groups, expansion, and Selberg’s 3/16 theorem

By: Quasirandom groups and a cheap version of the Brauer-Fowler theorem | What's new

Fri, 03 May 2013 00:28:42 +0000

[...] for groups, the modern study of which was initiated by Gowers, and is discussed for instance in this previous post. It gives the following slightly weaker version of Corollary [...]

By: Terence Tao

Terence Tao — Thu, 07 Feb 2013 16:12:54 +0000

You might find it easier to first establish the second conclusion (i.e. that whenever |G|^3/D' title='|A| |B| |C| > |G|^3/D' class='latex' />) before establishing the first (which is equivalent to the second).

By: Uwe Stroinski

Uwe Stroinski — Thu, 07 Feb 2013 08:09:37 +0000

Can you or a reader please help me with exercise 10. I can show the first inequality and I understand that one can use this to quantify that the number of places at which the convolution is small cannot be large. How does that help to prove the first inequality after ‘conclude in particular that’?

By: Uwe Stroinski

Uwe Stroinski — Mon, 17 Dec 2012 16:23:38 +0000

In the proof of Proposition 3 (mixing inequality) you write eigenvalue and mean eigenvalue .

[Corrected, thanks - T.]

By: Fred Lunnon

Fred Lunnon — Wed, 12 Dec 2012 13:37:30 +0000

Remark 3 : for “isocahedral symmetry” read “icosahedral symmetry” . WFL

[Corrected, thanks - T.]

By: Mixing for progressions in non-abelian groups « What’s new

Mixing for progressions in non-abelian groups « What’s new — Wed, 12 Dec 2012 05:04:16 +0000

[...] starting motivation for this paper was a question posed in this foundational paper of Tim Gowers on quasirandom groups. In that paper, Gowers showed (among other things) that if was a quasirandom group, patterns such [...]

By: Multiple recurrence in quasirandom groups « What’s new

Multiple recurrence in quasirandom groups « What’s new — Thu, 29 Nov 2012 01:32:02 +0000

[...] Geom. Func. Anal.. This paper builds upon a paper of Gowers in which he introduced the concept of a quasirandom group, and established some mixing (or recurrence) properties of such groups. A -quasirandom group is a [...]

By: 254B, Notes 7: Sieving and expanders « What’s new

254B, Notes 7: Sieving and expanders « What’s new — Fri, 02 Mar 2012 01:26:18 +0000

[...] a consequence of Proposition 4 of Notes 3, the following claim was shown: Proposition 7 Let be a -quasirandom finite group, is a [...]

By: 254B, Notes 6: Non-concentration in subgroups « What’s new

254B, Notes 6: Non-concentration in subgroups « What’s new — Tue, 14 Feb 2012 00:51:19 +0000

[...] the last three notes, we discussed the Bourgain-Gamburd expansion machine and two of its three ingredients, [...]

By: 254B, Notes 5: Product theorems, pivot arguments, and the Larsen-Pink non-concentration inequality « What’s new

Sun, 05 Feb 2012 19:32:56 +0000

[...] non-concentration, product theorems, and quasirandomness. Quasirandomness was discussed in Notes 3. In the current set of notes, we discuss product theorems. Roughly speaking, these theorems assert [...]