Project description
Exploring phase transitions and universal properties in random graphs
Supported by the Marie Skłodowska-Curie Actions programme, the GraPhTra project proposes to extend theoretical understanding of phase transitions and their universality in random graphs, while resolving several open questions. It will develop a new model for random graphs in neuromorphic computing, anticipating local energy factors, to demonstrate that the global structure of Gibbsian trees possesses a universal phase transition. For physics, it will determine conditions where the point of percolation phase transition on random unimodular graphs can firmly be predicted based on local information. In the case of epidemiology, it will resolve a long-standing question by demonstrating that long-range and scale-free percolation on spatial random graph models exhibit a phase with exponential neighbourhood growth
Objective
GraPhTra aims to advance the rigorous theoretical understanding of phase transitions in random graphs and their universal properties, driven by questions in neuromorphic computing, physics, and epidemiology. We will work on three work packages.
-We introduce a new model for random graphs, that are sampled with local energy considerations, inspired by statistical physics and motivated by material science for neuromorphic computing. We use a Gibbs measure to sample a spanning tree of a graph, and by varying the temperature we thus interpolate between the uniform spanning tree and the minimal spanning tree. We demonstrate that the global structure of Gibbsian trees (in the Gromov-Hausdorff-Prokhorov topology) exhibits a phase transition that is universal across various underlying graphs.
-We find conditions under which the position of the percolation phase transition on random unimodular graphs can be reliably estimated using local information. On the way, we resolve a key conjecture on the limiting threshold for Poisson–Voronoi percolation in hyperbolic space as the density of points goes to 0.
-We prove that the spatial random graph models ‘long-range percolation’ and ‘scale-free percolation’ possess a phase where neighbourhoods grow exponentially, ensuring a well-defined reproductive number for spatial SIR (Susceptible → Infected → Recovered) epidemics, answering a long-standing open question.
Fields of science (EuroSciVoc)
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.
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.
- medical and health sciences health sciences public health epidemiology
- natural sciences mathematics pure mathematics topology
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Keywords
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)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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)
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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
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.
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-2024-PF-01
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
9712CP Groningen
Netherlands
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