On the Shuffling Algorithm for Domino Tilings
Eric J. G. Nordenstam, Swedish Royal Institute of Technology (KTH)
Abstract
We study the dynamics of a certain discrete
model of interacting interlaced particles that comes from
the so called shuffling algorithm for sampling a
random tiling of an Aztec diamond.
It turns out that the transition probabilities
have 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.
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