On asymptotic behaviour of the degrees of vertices in a random graph

A random non-oriented graph with $n$ vertices is considered, in which the edge between the $i$-th and the $j$-th vertices ($i,j=1,2,\dots,n$; $i\ne j$) exists with a probability $p$ independently of the other edges. The asymptotic behaviour of the minimum and maximum degrees of vertices as $n\to\infty$, $p=p(n)\to0$ is studied.