caa a22 4500 445391855 CHVBK 20180317143049.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s10955-011-0121-2 doi (NATIONALLICENCE)springer-10.1007/s10955-011-0121-2 Interlaced Particle Systems and Tilings of the Aztec Diamond [Elektronische Daten] [Benjamin Fleming, Peter Forrester] 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 this particle system is exactly solvable, to the extent that not only can the partition function be computed exactly, but so too can the marginal distributions. These results in turn are used to give new derivations within the particle picture of a number of known fundamental properties of the tiling problem, for example that the number of distinct configurations is 2N(N+1)/2, and that there is a limit to the GUE minor process, which we show at the level of the joint PDFs. It is shown too that the study of tilings of the half Aztec diamond—not known from earlier literature—also leads to an interlaced particle system, now with successive lines 2n−1 and 2n (n=1, ,N/2−1) having n particles. Its exact solution allows for an analysis of the half Aztec diamond tilings analogous to that given for the Aztec diamond tilings. Springer Science+Business Media, LLC, 2011 Aztec diamond nationallicence Interlaced particle system nationallicence Tilings nationallicence Random matrices nationallicence Fleming Benjamin Department of Mathematics and Statistics, The University of Melbourne, 3010, Parkville, Victoria, Australia aut Forrester Peter Department of Mathematics and Statistics, The University of Melbourne, 3010, Parkville, Victoria, Australia aut Journal of Statistical Physics Springer US; http://www.springer-ny.com 142/3(2011-02-01), 441-459 0022-4715 142:3<441 2011 142 10955 https://doi.org/10.1007/s10955-011-0121-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-011-0121-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Fleming Benjamin Department of Mathematics and Statistics, The University of Melbourne, 3010, Parkville, Victoria, Australia aut NATIONALLICENCE 700 1- Forrester Peter Department of Mathematics and Statistics, The University of Melbourne, 3010, Parkville, Victoria, Australia aut NATIONALLICENCE 773 0- Journal of Statistical Physics Springer US; http://www.springer-ny.com 142/3(2011-02-01), 441-459 0022-4715 142:3<441 2011 142 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer