11 papers
Estimating the size of a set using cascading exclusion
Sourav Chatterjee, Persi Diaconis, Susan Holmes
Let be a finite set, and an i.i.d. uniform sample from . To estimate the size , without further structure, one can wait for repeats and use the birthda…
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…
Markov chains on Weyl groups from the geometry of the flag variety
Persi Diaconis, Calder Morton-Ferguson
This paper studies a basic Markov chain, the Burnside process, on the space of flags with and its upper triangular matrices. This gives rise to a…
Permuton and local limits for the Luce model
Jacopo Borga, Sourav Chatterjee, Persi Diaconis
We investigate the asymptotic properties of permutations drawn from the Luce model, a natural probabilistic framework in which permutations are generated sequentially by sampling w…
Random sampling of contingency tables and partitions: Two practical examples of the Burnside process
Persi Diaconis, Michael Howes
This paper gives new, efficient algorithms for approximate uniform sampling of contingency tables and integer partitions. The algorithms use the Burnside process, a general algorit…