Joanna Jasińska: Permuton limit of a generalization of the Mallows and k-card-minimum models скачать в хорошем качестве

Joanna Jasińska: Permuton limit of a generalization of the Mallows and k-card-minimum models

In my talk I will present a new random permutation model that unifies two classical families: the Mallows model and the k-card-minimum model of Travers. The model is defined via a sequential “card-picking” procedure in which, at each step, the next element is sampled from the remaining set according to a specified distribution. Under some natural assumptions on the sampling distribution, we prove that the associated sequence of random permutations converges (in probability) to a deterministic permuton. As a consequence, we obtain a weak law of large numbers for densities of finite permutation patterns. Finally, we establish a universality result for the band structure around the diagonal in the limiting permuton, confirming a conjecture of Travers for the k-card-minimum model. This talk will be based on my joint work with Balázs Ráth.