The product replacement algorithm and Kazhdan’s property (T)

  • Lubotzky A
  • Pak I
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Abstract

The “product replacement algorithm” is a commonly used heuristic to generate random group elements in a finite group G G , by running a random walk on generating k k -tuples of G G . While experiments showed outstanding performance, the theoretical explanation remained mysterious. In this paper we propose a new approach to the study of the algorithm, by using Kazhdan’s property (T) from representation theory of Lie groups.

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APA

Lubotzky, A., & Pak, I. (2000). The product replacement algorithm and Kazhdan’s property (T). Journal of the American Mathematical Society, 14(2), 347–363. https://doi.org/10.1090/s0894-0347-00-00356-8

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