  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 $\varepsilon>0$ 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 degree at least
$(1+\varepsilon)m_{d}(k,n)p$ 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.
