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October, 1995 Random Walks on the Groups of Upper Triangular Matrices
Richard Stong
Ann. Probab. 23(4): 1939-1949 (October, 1995). DOI: 10.1214/aop/1176987809

Abstract

This paper gives sharp bounds on the eigenvalues of a natural random walk on the group of upper triangular $n \times n$ matrices over the field of characteristic $p$, an odd prime, with 1's on the diagonal. In particular, this includes the finite Heisenberg groups as a special case. As a consequence we get bounds on the time required to achieve randomness for these walks. Some of the steps are done using the geometric bounds on the eigenvalues of Diaconis and Stroock. However, the crucial step is done using more subtle and idiosyncratic techniques. We bound the eigenvalues inductively over a sequence of subspaces.

Citation

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Richard Stong. "Random Walks on the Groups of Upper Triangular Matrices." Ann. Probab. 23 (4) 1939 - 1949, October, 1995. https://doi.org/10.1214/aop/1176987809

Information

Published: October, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0852.60076
MathSciNet: MR1379174
Digital Object Identifier: 10.1214/aop/1176987809

Subjects:
Primary: 60J10

Keywords: Eigenvalues , Random walk

Rights: Copyright © 1995 Institute of Mathematical Statistics

Vol.23 • No. 4 • October, 1995
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