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The two-periodic Aztec diamond and matrix valued orthogonal polynomials
- Publication Year :
- 2021
- Publisher :
- EUROPEAN MATHEMATICAL SOC-EMS, 2021.
-
Abstract
- We analyze domino tilings of the two-periodic Aztec diamond by means of matrix valued orthogonal polynomials that we obtain from a reformulation of the Aztec diamond as a non-intersecting path model with periodic transition matrices. In a more general framework we express the correlation kernel for the underlying determinantal point process as a double contour integral that contains the reproducing kernel of matrix valued orthogonal polynomials. We use the Riemann-Hilbert problem to simplify this formula for the case of the two-periodic Aztec diamond. In the large size limit we recover the three phases of the model known as solid, liquid and gas. We describe fine asymptotics for the gas phase and at the cusp points of the liquid-gas boundary, thereby complementing and extending results of Chhita and Johansson.<br />Comment: 80 pages, 20 figures; This is an extended version of the paper that is accepted for publication in the Journal of the EMS
- Subjects :
- Pure mathematics
General Mathematics
MODELS
Mathematics, Applied
Boundary (topology)
FOS: Physical sciences
RANDOM DOMINO TILINGS
01 natural sciences
SCHUR PROCESS
Christoffel–Darboux formula
Matrix (mathematics)
PEARCEY
FOS: Mathematics
Aztec diamond
0101 mathematics
Complex Variables (math.CV)
Mathematical Physics
CHRISTOFFEL-DARBOUX FORMULA
Mathematics
RIEMANN-HILBERT PROBLEMS
Science & Technology
Mathematics - Complex Variables
Applied Mathematics
010102 general mathematics
Probability (math.PR)
STRONG ASYMPTOTICS
Mathematical Physics (math-ph)
Methods of contour integration
STATISTICS
Kernel (image processing)
matrix valued orthogonal polynomials
Orthogonal polynomials
Physical Sciences
UNIVERSALITY
Determinantal point process
RESPECT
Mathematics - Probability
random tilings
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....35e51705c39b5f0919c1fa38532faeef