On the Shuffling Algorithm for Domino Tilings
2010 (English)In: Electronic Journal of Probability, ISSN 1083-6489, Vol. 15, 75-95 p.Article in journal (Refereed) Published
We study the dynamics of a certain discrete model of interacting interlaced particles that comes from the so called shuffling algorithm for sampling arandom tiling of an Aztec diamond. It turns out that the transition probabilitieshave a particularly convenient determinantal form. An analogous formula in a continuous setting has recently been obtained by Jon Warren studying certain model of interlacing Brownian motions which can be used to construct Dyson's non-intersecting Brownian motion.We conjecture that Warren's model can be recovered as a scaling limit of our discrete model and prove some partial results in this direction. As an application to one of these results we use it to rederive the known result that random tilings of an Aztec diamond, suitably rescaled near a turning point, converge to the GUE minor process.
Place, publisher, year, edition, pages
2010. Vol. 15, 75-95 p.
Aztec diamond, domino tilings, interlaced particles, GUE
IdentifiersURN: urn:nbn:se:kth:diva-9829ISI: 000273780800002ScopusID: 2-s2.0-77952804389OAI: oai:DiVA.org:kth-9829DiVA: diva2:133475
QC 201008042009-01-192009-01-122010-12-08Bibliographically approved