Dobrushin Conditions and Systematic Scan

We consider Glauber dynamics on finite spin systems. The mixing time of Glauber dynamics can be bounded in terms of the influences of sites on each other. We consider three parameters bounding these influences -- , the total influence on a site, as studied by Dobrushin; , the total influence of a site, as studied by Dobrushin and Shlosman; and , the total influence of a site in any given context, which is related to the pathcoupling method of Bubley and Dyer. It is known that if any of these parameters is less than 1 then random-update Glauber dynamics (in which a randomly-chosen site is updated at each step) is rapidly mixing. It is also known that the Dobrushin condition < 1 implies that systematic-scan Glauber dynamics (in which sites are updated in a deterministic order) is rapidly mixing. This paper studies two related issues, primarily in the context of systematic scan: (1) the relationship between the parameters , and , and (2) the relationship between proofs of rapid mix...

• Type: Conference
• Year: 2006
• Where: APPROX
• Authors: Martin E. Dyer, Leslie Ann Goldberg, Mark Jerrum
• Keywords: Algorithms, APPROX 2006, Glauber Dynamics, Rapid Mixing, Systematic Scan