On the size and complexity of connectivity components of a random hypergraph

The paper deals with finding the limit distributions of sizes and complexities of connectivity components of a random hypergraph in the binomial model Н(n,k,p). We consider the situation «inside the phase transition», when p = p(n) is equal to p = l/(k-1)(n-1) with l = l(n) satisfying the relation (l - 1)n1/3 ~ (k - 1)2/3а for fixed а G R. The main result is the generalization to Н(n,k,p) of the result of D. Aldous (1997) concerning the joint distributions of sizes and complexities of a random graph.