Can I read Grothendieck Shenanigans: Permutons from pipe dreams via integrable probability on EtoBox?

Grothendieck Shenanigans: Permutons from pipe dreams via integrable probability by Morales, Alejandro H.; Panova, Greta; Petrov, Leonid; Yeliussizov, Damir is a scholarly article available to read on EtoBox.

What is Grothendieck Shenanigans: Permutons from pipe dreams via integrable probability about?

We study random permutations arising from reduced pipe dreams. Our main model is motivated by Grothendieck polynomials with parameter $\beta=1$ arising in K-theory of the flag variety. The probability weight of a permutation is proportional to the principal specialization (setting all variables to 1) of the corresponding Grothendieck polynomial. By mapping this random permutation to a version of TASEP (Totally Asymmetric Simple Exclusion Process), we describe the limiting permuton and fluctuations around it as the order $n$ of the permutation grows to infinity. The fluctuations are of order $n^{\frac13}$ and have the Tracy-Widom GUE distribution, which places this algebraic (K-theoretic) model into the Kardar-Parisi-Zhang universality class. We also investigate non-reduced pipe dreams and make progress on a recent open problem on the asymptotic number of inversions of the resulting permutation. Inspired by Stanley's question for the maximal value of principal specializations of Schubert polynomials, we resolve the analogous question for $\beta=1$ Grothendieck polynomials, and provide bounds for general $\beta$.

Author

Morales, Alejandro H.; Panova, Greta; Petrov, Leonid; Yeliussizov, Damir

Published

2024

Language

EN