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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) 2015: 1.208
Source Normalized Impact per Paper (SNIP) 2015: 2.294
Impact per Publication (IPP) 2015: 1.103

Mathematical Citation Quotient (MCQ) 2015: 0.48

Online
ISSN
1869-6104
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Strong law of large numbers on graphs and groups

Natalia Mosina
  • Department of Mathematics, Engineering, and Computer Science, CUNY/LAGCC, Long Island City, NY, USA.
  • :
/ Alexander Ushakov
  • Department of Mathematics, Stevens Institute of Technology, Hoboken, NJ, USA.
  • :
Published Online: 2011-02-03 | DOI: https://doi.org/10.1515/gcc.2011.004

Abstract

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


Received: 2010-12-22

Published Online: 2011-02-03

Published in Print: 2011-05-01


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

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