## On Records: Scheduled Maxima Sequences and Longest Common Subsequences |

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argument c.f. Resnick CDG(m Chvatal and Sankoff co-ordinates collection continuous time process convergence in distribution cycle define definition denote digit pairs digits read Doctor of Philosophy drift E(number eligible pointer eligible region equations 1-36 expected number flowchart geometric distribution given hitting points homogeneous Poisson process i+l-N i=l i=l iid random variables ineligible integer k=l k=l law of large lim sup log cr log log longest common subsequence lower bound matched digit matches found matches obtained max-min sequence number of digits number of jumps number of matches pairs of digits permutation points of jump Poisson random measure process with rate random sequences random variables range sequence real number regular conditional distribution scheduled extremal process scheduled maxima sequence scheduling sequence sequence of random Skorohod subadditive ergodic theorem Suppose theorem V2n log vectors vlog weak convergence