Objective
This proposal aims to solve central open problems in the study of the Kardar–Parisi–Zhang (KPZ) class as well as develop new tools to study its models.
The KPZ class consists of a large set of models, sharing common microscopic dynamical features and aiming at modeling the physical phenomena of random growth interfaces. The two main goals in my proposal are
1) Show that the KPZ-scaling is universal in a large family of non-integrable models in the KPZ class.
It is believed that models in the KPZ class should converge, under what is called the KPZ-scaling, to a universal random object. Although widely believed, that the KPZ-scaling is universal is still largely conjectural and was shown mostly for a handful of exactly-solvable (integrable) models using deep connections to representation theory, combinatorics and random matrix theory. My plan is to show that, under the assumption of differentiability and curvature of the shape function, the KPZ-scaling exponents are universal in a large class of non-integrable models called Last Passage Percolation.
The principal tools to address this problem will be probabilistic-geometric in nature, using objects such as geodesics and ideas from queuing theory.
2) Construct a new limiting object that will open new paths to study the KPZ equation.
The KPZ equation is a central model in the KPZ class for a couple of reasons - firstly, it is believed to be the universal scaling limit in the intermediate disorder regime, and secondly, it is the crossover between two important physical phenomena - the Edwards-Wilkinson class and the KPZ class. I propose to introduce a new scaling limit that will shed light and enable us to study in new ways these two important aspects of the KPZ equation, as well provide new tools to address existing open problems.
To achieve this, I plan to take the perspective of scaling limits of random walks in random environment (RWRE), and develop new and complementing tools within that theory.
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.
You need to log in or register to use this function
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.
-
HORIZON.1.1 - European Research Council (ERC)
MAIN PROGRAMME
See all projects funded under this programme
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-ERC - HORIZON ERC Grants
See all projects funded under this funding scheme
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) ERC-2025-STG
See all projects funded under this callHost institution
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.
EH8 9YL Edinburgh
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.