We prove that given any $epsilon>0$, random integral $nimes n$ matriceswith independent entries that lie in any residue class modulo a prime withprobability at most $1-epsilon$ have cokernels asymptotically (as$nightarrowinfty$) distributed as in the distribution on finite abeliangroups that Cohen and Lenstra conjecture as the distribution for class groupsof imaginary quadratic fields. This is a refinement of a result on thedistribution of ranks of random matrices with independent entries in$mathbb{Z}/pmathbb{Z}$. This is interesting especially in light of the factthat these class groups are naturally cokernels of square matrices. We alsoprove the analogue for $nimes (n+u)$ matrices.
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机译：我们证明了给定的任何$ epsilon> 0 $，随机积分$ n times n $矩阵在任何残留类模型中的独立条目，它是最多$ 1- epsilon $的素数以1- epsilon $渐近地（AS $ n lightarrow Infty $）作为在有限的abeliangroups的分布中分发，Cohen和Lenstra猜想为虚拟二次领域的类组分配。这是一个完整的结果，即在$ mathbb {z} / p mathbb {z} $中具有独立条目的随机矩阵排名。这是有趣的，特别是鉴于这些类群体是平方矩阵的自然内科。我们为$ n times（n + u）$矩阵alsoprove。
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