Certifying numerical estimates of spectral gaps
Group Theory
2017-10-11 v3 Functional Analysis
Abstract
We establish a lower bound on the spectral gap of the Laplace operator on special linear groups using conic optimisation. In particular, this provides a constructive (but computer assisted) proof that these groups have Kazhdan property (T). A software for such optimisation for other finitely presented groups is provided.
Cite
@article{arxiv.1703.09680,
title = {Certifying numerical estimates of spectral gaps},
author = {Marek Kaluba and Piotr Nowak},
journal= {arXiv preprint arXiv:1703.09680},
year = {2017}
}
Comments
11 pages, 2 tables; minor changes, accepted in Groups Complexity Cryptology