6 papers · 1 filter
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…
A Vershik-Kerov theorem for wreath products
Sourav Chatterjee, Persi Diaconis
Let be the group of permutations of that permutes the first symbols arbitrarily, then the next symbols and so on through the last symbols…
Poisson approximation for large permutation groups
Persi Diaconis, Nathan Tung
Let be a group of permutations of objects which permutes things independently in disjoint blocks of size and then permutes the blocks. We investigate the probabi…
Counting the number of group orbits by marrying the Burnside process with importance sampling
Persi Diaconis, Chenyang Zhong
This paper introduces a novel and general algorithm for approximately counting the number of orbits under group actions. The method is based on combining the Burnside process and i…