Skip to main content
Go to the home page of the European Commission (opens in new window)
English en
CORDIS - EU research results
CORDIS

Towards Matching Bounds for Large Deviations

Project description

Making sense of unpredictable systems

A problem in physics and fluid mechanics is to predict how systems behave when they do not behave like we expect, for example, when rare fluctuations occur. There are theoretical frameworks to describe these types of behaviours, however they tend to apply to tidy and idealised situations. Supported by the Marie Skłodowska-Curie Actions programme, the TOMABOLD project will use recent breakthroughs to test when current theories still hold true. One part of the project will improve the theory to handle more complex systems; the other will explore cases where predictions fail. TOMABOLD aims to give scientists better tools to understand unpredictable systems – from small-scale phenomena to the chaotic nature of turbulent flows.

Objective

The proposed project considers the problem of finding matching bounds for dynamical large deviations of natural models in
statistical physics and fluid mechanics. In a random system with a deterministic limit, dynamical large deviations describe the
exponential decay of probability that the system is close to a trajectory different from the deterministic limit; classic works by Kipnis-
Olla-Varadhan and Kipnis-Landim study such bounds. However, in many interesting cases, the available upper and lower bounds only
agree when restricted to sufficiently regular trajectories.

Recent developments give the problem of investigating the matching bounds new momentum. On the positive side, Fehrman-Gess
reached an important milestone in matching bounds for hydrodynamic limits by analysis of a PDE, and proved matching bounds for a
family of SPDEs related to hydrodynamic limits. On the negative side, my previous work identified a case where the naïve bound is
not sharp, related the existence of spurious solutions violating the energy identity. We will capitalise on these recent developments
to identify cases where the expected rate function does, and does not, capture all interesting phenomena.

The project will be divided into two parts, taking these recent developments as a jumping off point. The first part will concern two examples where we expect to find matching bounds, while the second part investigates (anticipated) deviations from the classical theory. In WP1, we will investigate wide-reaching generalisations of Fehrman-Gess theory, in WP1a to the more challenging case of systems of equations, and in WP1b to rougher scaling regimes via the renormalisation group. In WP2, we will investigate one model which connects the existing counterexample to the derivation of turbulence from molecular dynamics, and another model in which we hypothesise that the violation of a key technical estimate leads to behaviour different from what is predicted in the literature.

Fields of science (EuroSciVoc)

Keywords

Programme(s)

Topic(s)

Funding Scheme

HORIZON-TMA-MSCA-PF-EF - HORIZON TMA MSCA Postdoctoral Fellowships - European Fellowships

See all projects funded under this funding scheme

Call for proposal

(opens in new window) HORIZON-MSCA-2024-PF-01

See all projects funded under this call

Coordinator

UNIVERSITETET I OSLO
Net EU contribution
€ 251 578,56
Address
PROBLEMVEIEN 5-7
0313 Oslo
Norway
Region
Norge Oslo og Viken Oslo
Activity type
Higher or Secondary Education Establishments
Links
Total cost
No data