4 papers
Schur--Weyl duality for diagonalizing a Markov chain on the hypercube
Persi Diaconis, Andrew Lin, Arun Ram
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 orthonorm…
A curiously slowly mixing Markov chain
Persi Diaconis, Andrew Lin, Arun Ram
We study a Markov chain with very different mixing rates depending on how mixing is measured. The chain is the "Burnside process on the hypercube ." Started at the all-zeros…
High-dimensional permutons: theory and applications
Jacopo Borga, Andrew Lin
Permutons, which are probability measures on the unit square with uniform marginals, are the natural scaling limits for sequences of (random) permutations. We introduce…
The Furstenberg property in Puiseux monoids
Andrew Lin, Henrick Rabinovitz, Qiao Zhang
Let be a commutative monoid. The monoid is called atomic if every non-invertible element of factors into atoms (i.e., irreducible elements), while is called a Furst…