Random Multiplication Approaches Uniform Measure in Finite Groups
نویسندگان
چکیده
منابع مشابه
2 00 4 Random Multiplication Approaches Uniform Measure in Finite Groups
In order to study how well a finite group might be generated by repeated random multiplications, P. Diaconis suggested the following urn model. An urn contains some balls labeled by elements which generate a group G. Two are drawn at random with replacement and a ball labeled with the group product (in the order they were picked) is added to the urn. We give a proof of his conjecture that the l...
متن کاملEfficient multiplication algorithms for finite polycyclic groups
Let G be a finite soluble group given by a reduced confluent polycyclic presentation. Represent group elements by reduced words. Then there exists an algorithm for multiplying two group elements which has subexponential running time and requires polynomial space. Moreover, given the prime factorisation of the group order, the problem of multiplying two group elements is probabilistically polyno...
متن کاملRandom Walks on Finite Groups
Markov chains on finite sets are used in a great variety of situations to approximate, understand and sample from their limit distribution. A familiar example is provided by card shuffling methods. From this viewpoint, one is interested in the “mixing time” of the chain, that is, the time at which the chain gives a good approximation of the limit distribution. A remarkable phenomenon known as t...
متن کاملGenerating Random Elements in Finite Groups
Let G be a finite group of order g. A probability distribution Z on G is called ε-uniform if |Z(x) − 1/g| ≤ ε/g for each x ∈ G. If x1, x2, . . . , xm is a list of elements of G, then the random cube Zm := Cube(x1, . . . , xm) is the probability distribution where Zm(y) is proportional to the number of ways in which y can be written as a product x1 1 x ε2 2 · · · xεm m with each εi = 0 or 1. Let...
متن کاملRandom walks in large finite groups
of random element is described means of ac<:oumtimg retllres:enl:ati'ves of certain of elements in finite groups (when the Pf()dllctilon or of such classes is restricted by the available cOlmputing resources), in the context of the some of the sp()ra,dlC finite groups.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Theoretical Probability
سال: 2007
ISSN: 0894-9840,1572-9230
DOI: 10.1007/s10959-006-0051-0