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Compositions of Random M
bius Transformations
Authors:
Satyajit Karmakar ab;
Eric S. Key c
| Affiliations: | a Department of Mathematics and Natural Sciences, Gordon College, Barnesville, Georgia, USA |
| b Department of Mathematics and Natural Sciences, Gordon College, Barnesville, GA, USA | |
| c Department of Mathematical Sciences, University of Wisconsin, Milwaukee, Wisconsin, USA |
DOI:
10.1081/SAP-120030445
Publication Frequency:
6 issues per year
Published in:
Stochastic Analysis and Applications,
Volume
22,
Issue
3
January
2005
, pages 525
- 557
Stochastic Analysis and Applications,
Volume
22,
Issue
3
January
2005
, pages 525
- 557
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(English)
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PDF
(English)
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Abstract
Let
 be a sequence of i.i.d. random variables taking values in the set of all M bius transformations. Consider the sequence  defined by  where z belongs to the extended complex plane. Necessary and sufficient conditions for a.s. convergence of will be discussed. As an application we will see how a sequence of the form may be used to generalize a mathematical model of phyllotaxis. Some results concerning the convergence in distribution of will also be discussed.
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Keywords:
Random Mbius transformations;
Phyllotaxis;
Cut-grow model
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