Statistics of reduced words in locally free and braid groups: Abstract studies and application to ballistic growth model

Details Statistics of reduced words in locally free and braid groups: Abstract studies and application to ballistic growth model Statistics of reduced words in locally free and braid groups: Abstract studies and application to ballistic growth model

1997-07-11

arxiv.org/abs/cond-mat/9707121v1

Physics

Condensed Matter

Statistical Mechanics

29 pages, LaTeX, 7 separated Postscript figures (available on request), submitted to J. Phys. (A): Math. Gen

Scientific paper

10.1088/0305-4470/31/12/004

We study numerically and analytically the average length of reduced (primitive) words in so-called locally free and braid groups. We consider the situations when the letters in the initial words are drawn either without or with correlations. In the latter case we show that the average length of the reduced word can be increased or lowered depending on the type of correlation. The ideas developed are used for analytical computation of the average number of peaks of the surface appearing in some specific ballistic growth model

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