Analysis of systematic scan Metropolis algorithms using Iwahori-Hecke algebra techniques
Analysis of systematic scan Metropolis algorithms using Iwahori-Hecke algebra techniques
math.RT↗
arXiv subjects
Persi Diaconis
Publications and source records attributed to Persi Diaconis.
The Poisson-Dirichlet law is the unique invariant distribution for uniform split-merge transformations
We consider a Markov chain on the space of (countable) partitions of the interval [0,1], obtained first by size biased sampling twice (allowing repetitions) and then merging the parts (if the sampled parts are distinct) or splitting the part uniformly (if the same part was sampled twice). We prove a conjecture of Vershik stating that the Poisson-Dirichlet law with parameter theta=1 is the unique invariant distribution for this Markov chain. Our proof uses a combination of probabilistic, combinatoric, and representation-theoretic arguments.
math.PR↗
The Asymmetric One-Dimensional Constrained Ising Model
We study a reversible one-dimensional spin system with Bernoulli(p) stationary distribution, in which a site can flip only if the site to its left is in state +1. Such models have been used as simple exemplars of systems exhibiting slow relaxation. We give fairly sharp estimates of the spectral gap as p decreases to zero. The method uses Poincare comparison with a long-range process which is analyzed by probabilistic methods (coupling, supermartingales).
math.PR↗