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An Exercise (?) in Fourier Analysis on the Heisenberg Group
- Source :
- Annales de la Faculté des Sciences de Toulouse. Mathématiques., Annales de la Faculté des Sciences de Toulouse. Mathématiques., Université Paul Sabatier _ Cellule Mathdoc 2017, 26 (2), pp.263-288, Annales de la Faculté des Sciences de Toulouse. Mathématiques., 2017, 26 (2), pp.263-288
- Publication Year :
- 2015
-
Abstract
- Let H(n) be the group of 3x3 uni-uppertriangular matrices with entries in Z/nZ, the integers mod n. We show that the simple random walk converges to the uniform distribution in order n^2 steps. The argument uses Fourier analysis and is surprisingly challenging. It introduces novel techniques for bounding the spectrum which are useful for a variety of walks on a variety of groups.<br />24 pages, 6 figures
- Subjects :
- Discrete mathematics
Uniform distribution (continuous)
Group (mathematics)
60J10, 60B15
Probability (math.PR)
010102 general mathematics
Spectrum (functional analysis)
General Medicine
01 natural sciences
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
symbols.namesake
Bounding overwatch
Fourier analysis
0103 physical sciences
FOS: Mathematics
Heisenberg group
symbols
Order (group theory)
010307 mathematical physics
0101 mathematics
Variety (universal algebra)
Mathematics - Probability
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 02402963 and 22587519
- Database :
- OpenAIRE
- Journal :
- Annales de la Faculté des Sciences de Toulouse. Mathématiques., Annales de la Faculté des Sciences de Toulouse. Mathématiques., Université Paul Sabatier _ Cellule Mathdoc 2017, 26 (2), pp.263-288, Annales de la Faculté des Sciences de Toulouse. Mathématiques., 2017, 26 (2), pp.263-288
- Accession number :
- edsair.doi.dedup.....5429096ddfaa8cfed2d0cfd9671f8559