MathDB3 problems
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Diaconis–Levin–Peres conjecture on Glauber dynamics and systematic-scan mixing times
Let a Gibbs sampler have Glauber dynamics, in which sites are updated randomly, and systematic scan dynamics, in which sites are updated in a fixed deterministic order. Measure the…
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Geometric-ergodicity implication from random-scan to deterministic Gibbs samplers
Let a two-variable Gibbs sampler have a random-scan Gibbs (RGS) chain and a deterministic Gibbs (DGS) chain targeting the same distribution. A Markov chain is geometrically ergodic…
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Uniqueness implies rapid mixing for antiferromagnetic Ising and hardcore models
Uniqueness–rapid-mixing conjecture. If uniqueness holds on the -regular tree for either model, then the Gibbs sampler is rapidly mixing on every graph of maximum degree for…