Thresholds for patterns in random permutations with a given number of inversions

We explore how the asymptotic structure of a random permutation of $[n]$ with $m$ inversions evolves, as $m$ increases, establishing thresholds for the appearance and disappearance of any classical, consecutive or vincular pattern. The threshold for the appearance of a classical pattern depends on the greatest number of inversions in any of its sum indecomposable components.

Bayesian Methods and Mixture Models Advanced Combinatorial Mathematics Stochastic processes and statistical mechanics

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