Project description
Study investigates integrable models in the KPZ universality class
The Kardar–Parisi–Zhang (KPZ) equation is a non-linear stochastic partial differential equation that has successfully been used to describe phenomena such as turbulence and interface growth processes that are far from equilibrium. Funded by the Marie Skłodowska-Curie Actions programme, the KPZcomb project aims to reveal fundamental properties of integrable models in the KPZ universality class at positive temperatures. Combining statistics, combinatorics and integrable systems, the study should allow deriving solutions in complex settings that involve restricted spatial geometries and multi-point correlation functions.
Objective
"The Kardar-Parisi-Zhang equation (KPZ) was introduced in 1986 as a universal model to capture statistics of a wide range of physical phenomena such as growth of interfaces or turbulent fluids. Remarkably fluctuations of this class of systems fall out of the scope of the classical central limit theorem. Understanding these phenomena has driven a tremendous activity in rigorous mathematics leading to groundbreaking theories or even to whole new fields such as that of Integrable Probability, where this proposal belongs.
Since the seminal work of Johansson (1999), it is understood that systems in the KPZ class are governed by distributions coming from random matrix theory. So far, a framework with clear ""determinantal structure"" has been created to tackle models at ""zero temperature"". Progress in positive temperature setting, including the KPZ equation, only came during the last decade. Insights from many different fields (combinatorics, symmetric functions, etc) into probability, allowed to treat one-point statistics of certain systems at positive temperature. In all instances a mysterious determinantal structure, whose origins elude understanding, appears to govern (so far only) one-point statistics.
This project aims to reveal the deep foundations of integrability of KPZ models at positive temperature and extend its scope. This will allow to settle the solvability in situations that are currently out of reach such as restricted spatial geometries and multi-point correlations. To achieve this we will follow a new route producing combinatorial mappings of positive temperature systems to purely determinantal ones. Our approach will make novel uses of methods from combinatorics and integrable systems (via the Yang-Baxter toolbox) and will create new dynamics linking integrable systems (such as box-ball system) to the KPZ universe. At the same time our probabilistic insights will give rise to new methodologies and will answer old questions from algebraic combinatorics"
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.
- natural sciences mathematics pure mathematics mathematical analysis differential equations
- natural sciences mathematics pure mathematics discrete mathematics combinatorics
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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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H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions
MAIN PROGRAMME
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H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility
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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.
MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)
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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) H2020-MSCA-IF-2020
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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.
CV4 8UW COVENTRY
United Kingdom
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.