121 citations · 1.4k across the 88 of their papers we have counts for
6 papers · 1 filter
Spectral gap for random-to-random shuffling on linear extensions
Arvind Ayyer, Anne Schilling, Nicolas M. Thiéry
In this paper, we propose a new Markov chain which generalizes random-to-random shuffling on permutations to random-to-random shuffling on linear extensions of a finite poset of si…
Crystal structure on rigged configurations and the filling map
Anne Schilling, Travis Scrimshaw
In this paper, we extend work of the first author on a crystal structure on rigged configurations of simply-laced type to all non-exceptional affine types using the technology of v…
Crystal approach to affine Schubert calculus
Jennifer Morse, Anne Schilling
We apply crystal theory to affine Schubert calculus, Gromov-Witten invariants for the complete flag manifold, and the positroid stratification of the positive Grassmannian. We intr…
Richard Stanley through a crystal lens and from a random angle
Anne Schilling
We review Stanley's seminal work on the number of reduced words of the longest element of the symmetric group and his Stanley symmetric functions. We shed new light on this by givi…
A uniform model for Kirillov-Reshetikhin crystals II. Alcove model, path model, and P=X
Cristian Lenart, Satoshi Naito, Daisuke Sagaki +2
We establish the equality of the specialization of the Macdonald polynomial at with the graded character of a tensor product of "single-column" Kirill…
Markov chains, -trivial monoids and representation theory
Arvind Ayyer, Anne Schilling, Benjamin Steinberg +1
We develop a general theory of Markov chains realizable as random walks on -trivial monoids. It provides explicit and simple formulas for the eigenvalues of the transit…