Jump to ContentJump to Main Navigation

Groups Complexity Cryptology

Managing Editor: Shpilrain, Vladimir / Weil, Pascal

Editorial Board Member: Blackburn, Simon R. / Conder, Marston / Dehornoy, Patrick / Eick, Bettina / Fine, Benjamin / Gilman, Robert / Grigoriev, Dima / Ko, Ki Hyoung / Kreuzer, Martin / Mikhalev, Alexander V. / Myasnikov, Alexei / Roman'kov, Vitalii / Rosenberger, Gerhard / Sapir, Mark / Schäge, Sven / Thomas, Rick / Tsaban, Boaz / Capell, Enric Ventura

2 Issues per year

SCImago Journal Rank (SJR) 2014: 0.917
Source Normalized Impact per Paper (SNIP) 2014: 1.559
Impact per Publication (IPP) 2014: 0.878

Mathematical Citation Quotient (MCQ) 2014: 0.37

Strong law of large numbers on graphs and groups

1Department of Mathematics, Engineering, and Computer Science, CUNY/LAGCC, Long Island City, NY, USA.

2Department of Mathematics, Stevens Institute of Technology, Hoboken, NJ, USA.

Citation Information: Groups – Complexity – Cryptology. Volume 3, Issue 1, Pages 67–103, ISSN (Online) 1869-6104, ISSN (Print) 1867-1144, DOI: 10.1515/gcc.2011.004, February 2011

Publication History

Published Online:


We consider (graph-)group-valued random element ξ, discuss the properties of a mean-set 𝔼(ξ), and prove the generalization of the strong law of large numbers for graphs and groups. Furthermore, we prove an analogue of the classical Chebyshev's inequality for ξ and Chernoff-like asymptotic bounds. In addition, we prove several results about configurations of mean-sets in graphs and discuss computational problems together with methods of computing mean-sets in practice and propose an algorithm for such computation.

Keywords.: Probability measures on graphs and groups; average; expectation; mean-set; strong law of large numbers; Chebyshev inequality; Chernoff bound; configuration of mean-sets; free group; shift search problem

Comments (0)

Please log in or register to comment.