Schur--Weyl duality for diagonalizing a Markov chain on the hypercube
Representation Theory
2025-12-30 v1 Combinatorics
Probability
Abstract
We show how the tools of modern algebraic combinatorics -- representation theory, Murphy elements, and particularly Schur--Weyl duality -- can be used to give an explicit orthonormal basis of eigenfunctions for a "curiously slowly mixing Markov chain" on the space of binary -tuples. The basis is used to give sharp rates of convergence to stationarity.
Cite
@article{arxiv.2512.23285,
title = {Schur--Weyl duality for diagonalizing a Markov chain on the hypercube},
author = {Persi Diaconis and Andrew Lin and Arun Ram},
journal= {arXiv preprint arXiv:2512.23285},
year = {2025}
}
Comments
Please feel free to make comments! This is a companion paper split off from arXiv:2511.01245, which originally contained the content of this work