On the chromatic numbers of random hypergraphs

The asymptotic behavior of the chromatic number of the binomial random hypergraph $H(n,k,p)$ is studied in the case when $k\ge4$ is fixed, $n$ tends to infinity, and $p=p(n)$ is a function. If $p=p(n)$ does not decrease too slowly, we prove that the chromatic number of $H(n,k,p)$ is concentrated in two or three consecutive values, which can be found explicitly as functions of $n$, $p$ and $k$.