### Abstract of "Random tilings and Markov chains for interlacing particles"

with Alexei Borodin.

We explain the relation between certain random tiling models and interacting

particle systems belonging to the anisotropic KPZ (Kardar-Parisi-Zhang)

universality class in *2+1*-dimensions. The link between these two *apriori* disjoint sets of models is a consequence of the presence of shuffling

algorithms that generate random tilings under consideration. To see the

precise connection, we represent both a random tiling and the corresponding

particle system through a set of non-intersecting lines, whose dynamics is

induced by the shuffling algorithm or the particle dynamics. The resulting class

of measures on line ensembles also fits into the framework of the Schur

processes.

Postscript file: [PS]

PDF file: [PDF]

arXiv: 1506.03910