Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, February 22, 2011, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Uli Wagner

An elementary construction of expanders

Constant degree expanders are graphs that are very sparse but nonetheless highly connected and that imitate many properties of the complete graph. For instance, they have "small" diameter, and a random walk in an expander "mixes quickly", i.e., we can i.e., after "few steps" the distribution of the random vertex we reach will approximate the uniform distribution of the set of vertices.

It is not hard to prove the existence of constant-degree expanders by probabilistic arguments. However, for many applications, one needs to be able to construct them in a way that is "explicit" (in a technical sense to be explained).

Beautiful explicit constructions of expanders were given by Margulis, and later by Gabber-Galil and by Lubotzky-Philips-Sarnak. These constructions are algebraic or number theoretic, and while the graphs are easy to describe, the proofs that they are, in fact, expanders are based on estimating the second eigenvalue of their adjacency matrices and, in some cases, rely on deep mathematical results.

Here, we present a simple iterative construction, due to Alon, Schwartz, and Shapira, for which both the construction and its analysis are rather elementary and combinatorial. The construction uses the notion of "replacement product" or "zig-zag product" due to Reingold, Vadhan, and Wigderson (with the basic idea going back to Gromov).

Upcoming talks     |     All previous talks     |     Talks by speaker     |     Upcoming talks in iCal format (beta version!)

Previous talks by year:   2024  2023  2022  2021  2020  2019  2018  2017  2016  2015  2014  2013  2012  2011  2010  2009  2008  2007  2006  2005  2004  2003  2002  2001  2000  1999  1998  1997  1996  

Information for students and suggested topics for student talks

Automatic MiSe System Software Version 1.4803M   |   admin login