The Cohen-Lenstra heuristic: Methodology and results

作者：Lengler Johannes^*

来源：Journal of Algebra, 2010, 323(10): 2960-2976.

DOI：10.1016/j.jalgebra.2010.01.016

• Cohen-Lenstra heuristic
• Probability measure
• Probability distribution
• Finite abelian groups
• Random matrices
• Class groups

In number theory, great efforts have been undertaken to study the Cohen-Lenstra probability measure on the set of all finite abelian p-groups. On the other hand, group theorists have studied a probability measure on the set of all partitions induced by the probability that a randomly chosen n x n-matrix over F(p) is contained in a conjugacy class associated with this partitions, for n -> infinity. This paper shows that both probability measures are identical. As a consequence, a multitude of results can be transferred from each theory to the other one. The paper contains a survey about the known methods to study the probability measure and about the results that have been obtained so far, from both communities.

• 出版日期2010-5-15