Interlaced particle systems and tilings of the Aztec diamond

Details Interlaced particle systems and tilings of the Aztec diamond Interlaced particle systems and tilings of the Aztec diamond

2010-04-03

arxiv.org/abs/1004.0474v1

Physics

Mathematical Physics

17 pages, 4 figures

Scientific paper

Motivated by the problem of domino tilings of the Aztec diamond, a weighted particle system is defined on $N$ lines, with line $j$ containing $j$ particles. The particles are restricted to lattice points from 0 to $N$, and particles on successive lines are subject to an interlacing constraint. It is shown that marginal distributions for this particle system can be computed exactly. This in turn is used to give unified derivations of a number of fundamental properties of the tiling problem, for example the evaluation of the number of distinct configurations and the relation to the GUE minor process. An interlaced particle system associated with the domino tiling of a certain half Aztec diamond is similarly defined and analyzed.

Affiliated with

Also associated with

No associations

Rating

Interlaced particle systems and tilings of the Aztec diamond does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Interlaced particle systems and tilings of the Aztec diamond, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Interlaced particle systems and tilings of the Aztec diamond will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-448725