Record-biased permutations and their permuton limit

Abstract In this article, we study a non-uniform distribution on permutations biased by their number of records that we call record-biased permutations . We give several generative processes for record-biased permutations, explaining also how they can be used to devise efficient (linear) random samplers. For several classical permutation statistics, we obtain their expectation using the above generative processes, as well as their limit distributions in the regime that has a logarithmic number of records (as in the uniform case). Finally, increasing the bias to obtain a regime with an expected linear number of records, we establish the convergence of record-biased permutations to a deterministic permuton, which we fully characterise. This model was introduced in our earlier work [3], in the context of realistic analysis of algorithms. We conduct here a more thorough study but with a theoretical perspective.