Statistical Properties of Locally Free Groups¶with Applications to Braid Groups¶and Growth of Random Heaps |
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| Authors: | A M Vershik S Nechaev R Bikbov |
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| Institution: | (1) St. Petersburg Branch of Steklov Mathematical Institute, Fontanka 27, 119011 St. Petersburg, Russia, RU;(2) UMR 8626, CNRS - Université Paris XI, LPTMS, Bat. 100, Université Paris Sud, 91405 Orsay Cedex, France, FR;(3) L.D. Landau Institute for Theoretical Physics, Kosygin str. 2, 117940 Moscow, Russia, US |
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| Abstract: | The main statistical characteristics of locally free groups: the growth, the drift and the entropy are considered and relations
between them are established. Our results assert that: (i) the statistical properties of random walks (Markov chains) on locally
free and braid groups are not the same as the uniform statistics on these groups, and (ii) the stabilization of the statistical
characteristics exists when the number of generators of the group grows.
Received: 7 June 1999 / Accepted: 21 April 2000 |
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