0 Non - Intersecting Paths , Random Tilings and Random Matrices
نویسنده
چکیده
We investigate certain measures induced by families of non-intersecting paths in domino tilings of the Aztec diamond, rhombus tilings of an abc-hexagon, a dimer model on a cylindrical brick lattice and a growth model. The measures obtained, e.g. the Krawtchouk and Hahn ensembles, have the same structure as the eigenvalue measures in random matrix theory like GUE, which can in fact can be obtained from non-intersecting Brownian motions. The derivations of the measures are based on the Karlin-McGregor or Lindström-Gessel-Viennot method. We use the measures to show some asymptotic results for the models.
منابع مشابه
Symmetrized models of last passage percolation and non-intersecting lattice paths
It has been shown that the last passage time in certain symmetrized models of directed percolation can be written in terms of averages over random matrices from the classical groups U(l), Sp(2l) and O(l). We present a theory of such results based on non-intersecting lattice paths, and integration techniques familiar from the theory of random matrices. Detailed derivations of probabilities relat...
متن کاملRandom Matrices and Determinantal Processes
Eigenvalues of random matrices have a rich mathematical structure and are a source of interesting distributions and processes. These distributions are natural statistical models in many problems in quantum physics, [15]. They occur for example, at least conjecturally, in the statistics of spectra of quantized models whose classical dynamics is chaotic, [4]. Random matrix statistics is also seen...
متن کاملRandom Matrix Models, Non-intersecting random paths, and the Riemann-Hilbert Analysis
Random matrix theory (RMT) is a very active area of research and a great source of exciting and challenging problems for specialists in many branches of analysis, spectral theory, probability and mathematical physics. The analysis of the eigenvalue distribution of many random matrix ensembles leads naturally to the concepts of determinantal point processes and to their particular case, biorthog...
متن کاملAlternating sign matrices and tilings of Aztec rectangles
The problem of counting numbers of tilings of certain regions has long interested researchers in a variety of disciplines. In recent years, many beautiful results have been obtained related to the enumeration of tilings of particular regions called Aztec diamonds. Problems currently under investigation include counting the tilings of related regions with holes and describing the behavior of ran...
متن کاملPfaffian Algorithms for Sampling Routings on Regions with Free Boundary Conditions
Sets of non-intersecting, monotonic lattice paths, or xed routings, provide a common representation for several combinatorial problems and have been the key element for designing sampling algorithms. Markov chain algorithms based on routings have led to eecient samplers for tilings, Eulerian orientations 8] and triangulations 9], while an algorithm which successively calculates ratios of determ...
متن کامل