@article{74468f26e7934f7e9d075811bdffedda,
title = "Character ratios, representation varieties and random generation of finite groups of Lie type",
abstract = "We use character theory of finite groups of Lie type to establish new results on representation varieties of Fuchsian groups, and also on probabilistic generation of groups of Lie type.",
keywords = "Fuchsian groups, Random generation, Representation varieties",
author = "Liebeck, {Martin W.} and Aner Shalev and Tiep, {Pham Huu}",
note = "Funding Information: The first and second authors acknowledge the support of EPSRC grant EP/H018891/1. The second author acknowledges the support of ERC advanced grant 247034, ISF grants 1117/13 and 686/17, BSF grant 2016072, and the Vinik chair of mathematics which he holds. The third author was partially supported by the NSF grant DMS-1839351 and DMS-1840702, the Simons Foundation Fellowship 305247, the EPSRC, the Mathematisches Forschungsinstitut Oberwolfach, and the Joshua Barlaz Chair in Mathematics. Parts of the paper were written while the third author visited the Departments of Mathematics of Imperial College London, and University of Chicago. It is a pleasure to thank Imperial College, Prof. Ngo Bao Chau, and the University of Chicago for generous hospitality and stimulating environment. The authors are grateful to the referee for insightful comments on the paper. Funding Information: The first and second authors acknowledge the support of EPSRC grant EP/H018891/1 . The second author acknowledges the support of ERC advanced grant 247034 , ISF grants 1117/13 and 686/17 , BSF grant 2016072 , and the Vinik chair of mathematics which he holds. The third author was partially supported by the NSF grant DMS-1839351 and DMS-1840702 , the Simons Foundation Fellowship 305247 , the EPSRC , the Mathematisches Forschungsinstitut Oberwolfach , and the Joshua Barlaz Chair in Mathematics . Parts of the paper were written while the third author visited the Departments of Mathematics of Imperial College London, and University of Chicago. It is a pleasure to thank Imperial College, Prof. Ngo Bao Chau, and the University of Chicago for generous hospitality and stimulating environment. The authors are grateful to the referee for insightful comments on the paper. Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",
year = "2020",
month = nov,
day = "18",
doi = "10.1016/j.aim.2020.107386",
language = "English (US)",
volume = "374",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press Inc.",
}