On the intersecting family process

Abstract

We study the intersecting family process initially studied in \cite{BCFMR}. Here $k=k(n)$ and $E_1,E_2,\dots ,E_m$ is a random sequence of $k$-sets from $\left(\genfrac{}{}{0ex}{}{[n]}{k}\right)$ where $E_{r+1}$ is uniformly chosen from those $k$-sets that are not already chosen and that meet $E_i,i=1,2,\dots ,r$. We prove some new results for the case where $k=c{n}^{1/3}$ and for the case where $k\gg n^{1/2}$.