%0 Journal Article %T A probabilistic approach to the asymptotics of the length of the longest alternating subsequence %A Christian Houdr¨¦ %A Ricardo Restrepo %J Mathematics %D 2010 %I arXiv %X Let $LA_{n}(\tau)$ be the length of the longest alternating subsequence of a uniform random permutation $\tau\in[n]$. Classical probabilistic arguments are used to rederive the asymptotic mean, variance and limiting law of $LA_{n}(\tau)$. Our methodology is robust enough to tackle similar problems for finite alphabet random words or even Markovian sequences in which case our results are mainly original. A sketch of how some cases of pattern restricted permutations can also be tackled with probabilistic methods is finally presented. %U http://arxiv.org/abs/1005.1893v2