I will first provide a panorama of various recent and not so recent results (due to various authors) on the asymptotics, in mean, variance and limiting law, for the length of some subsequence problems. Then, I will describe a recent result in the following framework: Let $X_1, X_2,dots, X_n,dots$ and $Y_1, Y_2,dots, Y_ndots$ be two independent sequences of iid random variables taking their values in a common ordered alphabet. Let LCI$_n$ be the length of the longest common and increasing subsequence of $X_1,dots, X_n$ and $Y_1,dots, Y_n$. As $n$ grows without bound, and when properly centered and normalized, LCI$_n$ is shown to converge, in distribution, towards a Brownian functional that we identify.
Speaker: Christian Houdre, School of Mathematics, Georgia Institute of Technology