An Erd\H os Rényi Law for the Longest Consecutive Monotone Block in a Random Permutation

Anant Godbole

The Erd\H os-Rényi law states that given a sequence $\{X_j{\}}_{j=1}^{\infty }$ of i.i.d.~($p$) coin-tosses, the longest run $L_n$ of heads in the first $n$ coin tosses approaches $\lo…