Mallows permutations avoiding a length-3 pattern with bias e^{β/n} converge to a non-trivial explicit deterministic permuton depending on the pattern and β, with accompanying LDP and q-Catalan asymptotics.
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Large deviation principles for pattern-avoiding permutations, and limit shapes for constrained Mallows permutations
Mallows permutations avoiding a length-3 pattern with bias e^{β/n} converge to a non-trivial explicit deterministic permuton depending on the pattern and β, with accompanying LDP and q-Catalan asymptotics.