Project description
From random tilings to disordered physical systems
Even tiny imperfections in materials can influence how they behave on a much larger scale. Supported by the Marie Skłodowska-Curie Actions programme, the Aztec RHP project will study a stochastic version of the Aztec diamond tiling model in which the rules governing domino arrangements are random. Its aim is to improve understanding of how disorder influences the behaviour of physical systems, including magnetic and conductive materials. The project will analyse a novel class of random Riemann-Hilbert problems, an advanced mathematical framework used to study patterns and large-scale behaviour in complex systems. In doing so, Aztec RHP will further develop the theory of random Riemann-Hilbert problems, bridging random tiling theory and integrable probability while expanding the mathematical tools.
Objective
The Aztec diamond is a random tiling model whereby a diamond-shaped region is randomly tiled with 1x2 and 2x1 dominos. While simple, this model serves as an important toy problem for the emergence of various phenomenon that have been observed in physical systems of interest, like the six-vertex model or the Ising model. The novelty considered in the present proposal is the particular choice of the model's parameters (or weights); namely we take these weights to be themselves random. The motivation for this choice lies in the fact that random weights are expected to model physical systems with impurities. A topic of great practical importance, as impurities are not only ubiquitous in all condensed matter systems, but also influence key physical properties like conductance or magnetism.
The method of choice for the present proposal is primarily the Riemann-Hilbert approach. This is a powerful complex analytic technique to study various problems in asymptotic analysis, and has been used in recent years with great success in the study of a variety of models of the Aztec diamond. However, so far the case of random weights was not considered using this approach. It should be emphasized that the choice of random weights presented here will naturally lead to a random Riemann-Hilbert problem. Such problems appeared only recently in the analysis of soliton gases, but so far not in the context of random tilings. Thus, one of the aims of the present proposal is to further develop the theory of random Riemann-Hilbert problems in this new context, thereby extending the reach of the Riemann-Hilbert method.
Fields of science (EuroSciVoc)
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CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
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Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
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Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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HORIZON.1.2 - Marie Skłodowska-Curie Actions (MSCA)
MAIN PROGRAMME
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Topic(s)
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Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
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Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
HORIZON-TMA-MSCA-PF-EF - HORIZON TMA MSCA Postdoctoral Fellowships - European Fellowships
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Call for proposal
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Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) HORIZON-MSCA-2025-PF
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DH1 3LE DURHAM
United Kingdom
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