Random groups and Property (T): Żuk's theorem revisited

Details Random groups and Property (T): Żuk's theorem revisited Random groups and Property (T): Żuk's theorem revisited

2011-06-11

arxiv.org/abs/1106.2242v1

Mathematics

Group Theory

Scientific paper

We provide a full and rigorous proof of a theorem attributed to \.Zuk, stating that random groups in the Gromov density model for d > 1/3 have property (T) with high probability. The original paper had numerous gaps, in particular, crucial steps involving passing between different models of random groups were not described. We fix the gaps using combinatorial arguments and a recent result concerning perfect matchings in random hypergraphs. We also provide an alternative proof, avoiding combinatorial difficulties and relying solely on spectral properties of random graphs in G(n, p) model.

Affiliated with

Also associated with

No associations

Rating

Random groups and Property (T): Żuk's theorem revisited does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Random groups and Property (T): Żuk's theorem revisited, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Random groups and Property (T): Żuk's theorem revisited will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-414323