Leírás
A modern approach to discrete objects is studying their appropriately defined analytic limits. In an ideal case, mathematical energy can flow in both directions meaningfully: not simply discrete statements have analytic counterparts, but statements in the infinite world have nontrivial corollaries in the finite.
The standard theory of permutation limits concerns permutons, which are probability measures on the unit square with uniform marginals. After introducing the core concepts and in what metric permutations converge to a permuton, in my talk I study the question how well a given permuton can be approximated by length n permutations. In this generality, the question turns out to be essentially equivalent to classical questions of measure theoretic discrepancy theory, while questions concerning subsequential approximations truly require further analysis.