Longest increasing subsequences in Luce permutations, using permuton theory
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ENS de Lyon
The Luce model is an interesting distribution on permutations, originally motivated by psychophysics experiments.
Despite its conceptual simplicity, its emergence under many forms, and its widespread usage in applications, the (asymptotic) behavior of the Luce model remains largely misunderstood.
Independently, permuton theory was introduced as a scaling limit framework for large (random) permutations.
Informally, the convergence of a sequence of permutations towards a permuton tells you "where the points of the permutations tend to be", on a macroscopic scale.
This simplicity is both a strength (proving a permuton convergence is relatively simple) and a weakness (the direct consequences are modest).
In the last decade, an emerging line of research has been to complement permuton convergence with appropriate "regularity properties" and deduce powerful consequences.
In this talk I will explain why this philosophy applies to the Luce model, and how permuton theory can be used to study their longest increasing subsequences.