TY - JOUR
T1 - Exact solutions for KPZ-type growth processes, random matrices, and equilibrium shapes of crystals
AU - Spohn, Herbert
PY - 2006/9/1
Y1 - 2006/9/1
N2 - Three models from statistical physics can be analyzed by employing space-time determinantal processes: (1) crystal facets, in particular the statistical properties of the facet edge, and equivalently tilings of the plane, (2) one-dimensional growth processes in the Kardar-Parisi-Zhang universality class and directed last passage percolation, (3) random matrices, multi-matrix models, and Dyson's Brownian motion. We explain the method and survey results of physical interest.
AB - Three models from statistical physics can be analyzed by employing space-time determinantal processes: (1) crystal facets, in particular the statistical properties of the facet edge, and equivalently tilings of the plane, (2) one-dimensional growth processes in the Kardar-Parisi-Zhang universality class and directed last passage percolation, (3) random matrices, multi-matrix models, and Dyson's Brownian motion. We explain the method and survey results of physical interest.
KW - Determinantal processes
KW - Edge scaling
KW - Matrix-valued Brownian motion
UR - http://www.scopus.com/inward/record.url?scp=33745660065&partnerID=8YFLogxK
U2 - 10.1016/j.physa.2006.04.006
DO - 10.1016/j.physa.2006.04.006
M3 - Article
AN - SCOPUS:33745660065
SN - 0378-4371
VL - 369
SP - 71
EP - 99
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
IS - 1
ER -