Generating Random Elements in SLn (Fq) by Random Transvections

Martin Hildebrand

doi:10.1023/A:1022472220105

Generating Random Elements in SL_n (F_q) by Random Transvections

Martin Hildebrand

Mathematics and Statistics

University at Albany

Research output: Contribution to journal › Article › peer-review

29 Scopus citations

Abstract

This paper studies a random walk based on random transvections in SL_n(F_q) and shows that, given (Formula presented.) > 0, there is a constant c such that after n + c steps the walk is within a distance (Formula presented.) from uniform and that after n − c steps the walk is a distance at least 1 − (Formula presented.) from uniform. This paper uses results of Diaconis and Shahshahani to get the upper bound, uses results of Rudvalis to get the lower bound, and briefly considers some other random walks on SL_n(F_q) to compare them with random transvections.

Original language	English
Pages (from-to)	133-150
Number of pages	18
Journal	Journal of Algebraic Combinatorics
Volume	1
Issue number	2
DOIs	https://doi.org/10.1023/A:1022472220105
State	Published - Sep 1992

Keywords

random walk
representation theory
transvection
upper bound lemma

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10.1023/A:1022472220105

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abstract = "This paper studies a random walk based on random transvections in SLn(Fq) and shows that, given (Formula presented.) > 0, there is a constant c such that after n + c steps the walk is within a distance (Formula presented.) from uniform and that after n − c steps the walk is a distance at least 1 − (Formula presented.) from uniform. This paper uses results of Diaconis and Shahshahani to get the upper bound, uses results of Rudvalis to get the lower bound, and briefly considers some other random walks on SLn(Fq) to compare them with random transvections.",

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AB - This paper studies a random walk based on random transvections in SLn(Fq) and shows that, given (Formula presented.) > 0, there is a constant c such that after n + c steps the walk is within a distance (Formula presented.) from uniform and that after n − c steps the walk is a distance at least 1 − (Formula presented.) from uniform. This paper uses results of Diaconis and Shahshahani to get the upper bound, uses results of Rudvalis to get the lower bound, and briefly considers some other random walks on SLn(Fq) to compare them with random transvections.

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KW - representation theory

KW - transvection

KW - upper bound lemma

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ER -

Generating Random Elements in SL_n (F_q) by Random Transvections

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