  The theme of this paper is the derivation of analytic formulae for certain
large combinatorial structures. The formulae are obtained via fluid limits of
pure jump-type Markov processes, established under simple conditions on the
Laplace transforms of their Levy kernels. Furthermore, a related Gaussian
approximation allows us to describe the randomness which may persist in the
limit when certain parameters take critical values. Our method is quite
general, but is applied here to vertex identifiability in random hypergraphs. A
vertex v is identifiable in n steps if there is a hyperedge containing v all of
whose other vertices are identifiable in fewer steps.
  We say that a hyperedge is identifiable if every one of its vertices is
identifiable. Our analytic formulae describe the asymptotics of the number of
identifiable vertices and the number of identifiable hyperedges for a
Poisson(\beta) random hypergraph \Lambda on a set V of N vertices, in the limit
as N\to \infty. Here \beta is a formal power series with nonnegative
coefficients \beta_0,\beta_1,..., and (\Lambda(A))_{A\subseteq V} are
independent Poisson random variables such that \Lambda(A), the number of
hyperedges on A, has mean N\beta_j/\pmatrixN j whenever |A|=j.
