Project description
Reaching equilibrium in disordered environments
Many systems in nature and society can be described using mathematical models called Markov chains, including particles moving in a fluid or people exchanging information. These systems gradually reach a stable state or equilibrium. With the support of the Marie Skłodowska-Curie Actions programme, the PARTYMIX project aims to study how long it takes for such systems to settle and whether the change happens smoothly or abruptly. Researchers will explore how random irregularities in the environment influence stability, deepening our understanding of complex systems. Project findings have the potential to advance new mathematical tools for studying randomness in dynamic processes.
Objective
A fundamental result in probability theory states that the distribution of an irreducible, time continuous Markov chain on a finite state space converges to an equilibrium as time tends to infinity. The study of Markov chain mixing time is a branch of Probability Theory that tries to understand the characteristic of this convergence and answer questions such as: How much time is needed to converge to equilibrium? Is the convergence regular or abrupt?
Within this field only little effort have been made to understand how random inhomogeneities can affect the pattern of convergence to equilibrium. The objective of our research project is to develop the mathematical understanding of relaxation to equilibrium of disordered systems. To do so, we will explore in depth the case of a specific disordered model - the Simple Exclusion Process (SEP) in a random environment - with the hindsight of developing robust methods which contribute to the understanding of disordered Markov processes.
Our project defines a handful of precise scientific questions on which our efforts should be focused. These concern the asymptotic behavior, as the system size go to infinity, of the spectral gap and of the mixing time for disordered Simple Exclusion Process on one dimensional graphs as well as the possible occurrence of the cutoff phenomenon for the process.
Fields of science (EuroSciVoc)
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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)
MAIN PROGRAMME
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Topic(s)
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.
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
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
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.
00154 ROMA
Italy
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.