For positive integers $d<k$ and n divisible by k, let $m_d(k,n)$ be the minimum d-degree ensuring the existence of a perfect matching in a k-uniform hypergraph. In the graph case (where $k=2$), a classical theorem of Dirac says that $m_1(2,n)=\lceil n/2\rceil$. However, in general, our understanding of the values of $m_d(k,n)$ is still very limited, and it is an active topic of research to determine or approximate these values. In this paper we prove a “transference” theorem for Dirac-type results relative to random hypergraphs. Specifically, for any $d<k$, any $\epsilon >0$ and any “not too small” p, we prove that a random k-uniform hypergraph G with n vertices and edge probability p typically has the property that every spanning subgraph of G with minimum d-degree at least $(1+\epsilon )m_d(k,n)p$ has a perfect matching. One interesting aspect of our proof is a “non-constructive” application of the absorbing method, which allows us to prove a bound in terms of $m_d(k,n)$ without actually knowing its value.

对于正整数$d<ķ$和n可被k整除，让${米}_d(ķ,n)$是确保在k均匀超图中存在完美匹配的最小d度。在图形情况下（其中$ķ=2$)，狄拉克的一个经典定理说${米}_1(2,n)=\lceil n/2\rceil$. 然而，总的来说，我们对价值观的理解${米}_d(ķ,n)$仍然非常有限，确定或近似这些值是一个活跃的研究课题。在本文中，我们证明了相对于随机超图的狄拉克类型结果的“转移”定理。具体来说，对于任何$d<ķ$， 任何$\epsilon >0$和任何“不太小”的p，我们证明具有n个顶点和边概率p的随机k均匀超图G通常具有以下性质：G的每个生成子图至少具有最小d度$(1+\epsilon ){米}_d(ķ,n)p$有一个完美的匹配。我们证明的一个有趣的方面是吸收方法的“非建设性”应用，它允许我们证明一个界限${米}_d(ķ,n)$在不知道它的价值的情况下。