Large deviations for increasing subsequences of permutations and a concurrency application

The study of concurrent processes with conflict points is connected with the geometry of increasing subsequences of permutations - a permutation encodes the transactions of two processes that conflict (i.e., must be executed serially), and a given increasing subsequence encodes one particular serialization of the executions of two processes. This motivates the study of random increasing subsequences of random permutations. Here, we give a large deviation principle which implies that such a subsequence never deviates too far from the identity permutation: a random serialization of two concurrent processes will not favor either process too much at any given time. We then give an efficient exact algorithm for uniform random sampling of an increasing subsequence from a given permutation.