Distributions of permutations generated by inhomogeneous Markov chains

  • This work connects Markov chain imbedding technique (MCIT) introduced by M.V. Koutras and J.C. Fu with distributions concerning the cycle structure of permutations. As a final result program code is given that uses MCIT to deliver proper numerical values for these. The discrete distributions of interest are the one of the cycle structure, the one of the number of cycles, the one of the rth longest and shortest cycle and finally the length of a random chosen cycle. These are analyzed for equiprobable permutations as well as for biased ones. Analytical solutions and limit distributions are also considered to put the results on a safe, theoretical base.

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Author:Thomas Theobald
Advisor:Ralph Neininger
Document Type:diplomthesis
Date of Publication (online):2010/01/29
Year of first Publication:2009
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Granting Institution:Johann Wolfgang Goethe-Universität
Release Date:2010/01/29
Tag:Markov chain imbedding technique; cycle structure of permutations
GND Keyword:Markov-Kette; Permutation; Einbettung <Mathematik>
Institutes:Informatik und Mathematik / Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):License LogoDeutsches Urheberrecht