The product replacement algorithm and Kazhdan’s property (T)
نویسندگان
چکیده
منابع مشابه
The Product Replacement Algorithm and Kazhdan’s Property (t)
A problem of great importance in computational group theory is to generate (nearly) uniformly distributed random elements in a finite groupG. A good example of such an algorithm should start at any given set of generators, use no prior knowledge of the structure of G, and in a polynomial number of group operations return the desired random group elements (see [Bb2]). Then these random elements ...
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The product replacement algorithm is a heuristic designed to generate random group elements. The idea is to run a random walk on generating k-tuples of the group, and then output a random component. The algorithm was designed by Leedham-Green and Soicher ([31]), and further investigated in [12]. It was found to have an outstanding performance, much better than the the previously known algorithm...
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The product replacement algorithm is a commonly used heuristic to generate random group elements in a finite group G, by running a random walk on generating k-tuples of G. While experiments showed outstanding performance, until recently there was little theoretical explanation. We give an extensive review of both positive and negative theoretical results in the analysis of the algorithm.
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The \product replacement algorithm" is a commonly used heuristic to generate random group elements in a nite group G, by running a random walk on generating k-tuples of G. While experiments showed outstanding performance, the theoretical explanation remained mysterious. In this paper we propose a new approach to study of the algorithm, by using Kazhdan's property (T) from representation theory ...
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ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 2000
ISSN: 0894-0347,1088-6834
DOI: 10.1090/s0894-0347-00-00356-8