Asymptotics of random domino tilings of rectangular Aztec diamonds
Alexey Bufetov,Alisa Knizel +1 more
TLDR
In this article, asymptotics of a domino tiling model on a class of domains which are called rectangular Aztec diamonds are considered and the Law of Large Numbers for the corresponding height functions and explicit formulas for the limit are provided.Abstract:
We consider asymptotics of a domino tiling model on a class of domains which we call rectangular Aztec diamonds. We prove the Law of Large Numbers for the corresponding height functions and provide explicit formulas for the limit. For a special class of examples, the explicit parametrization of the frozen boundary is given. It turns out to be an algebraic curve with very special properties. Moreover, we establish the convergence of the fluctuations of the height functions to the Gaussian Free Field in appropriate coordinates. Our main tool is a recently developed moment method for discrete particle systems.read more
Citations
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Book ChapterDOI
Lectures on the Combinatorics of Free Probability: The free commutator
Alexandru Nica,Roland Speicher +1 more
Journal ArticleDOI
Fluctuations of particle systems determined by Schur generating functions
TL;DR: In this paper, a new toolbox for the analysis of the global behavior of stochastic discrete particle systems has been developed, based on the notion of the Schur generating function of a random discrete configuration.
Journal ArticleDOI
Arctic curves of the six-vertex model on generic domains: the Tangent Method
Filippo Colomo,Andrea Sportiello +1 more
TL;DR: In this article, the authors revisited the problem of determining the Arctic curve in the six-vertex model with domain wall boundary conditions and proposed an alternative method, by which they recover the previously conjectured analytic expression in the square domain.
Journal ArticleDOI
Fourier transform on high-dimensional unitary groups with applications to random tilings
Alexey Bufetov,Vadim Gorin +1 more
TL;DR: In this article, a combination of direct and inverse Fourier transforms on the unitary group U(N) identifies normalized characters with probability measures on N-tuples of integers.
References
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Lectures on the Combinatorics of Free Probability
Alexandru Nica,Roland Speicher +1 more
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