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From Liouville to Kolmogorov: 2d quantum gravity, noise sensitivity and turbulent flows

Total Cost €


EC-Contrib. €






 LiKo project word cloud

Explore the words cloud of the LiKo project. It provides you a very rough idea of what is the project "LiKo" about.

object    attempt    statistical    conjecturally    maps    special    kolmogorov    construct    near    tools    area    genuine    embeddings    combinatorial    packings    smirnov    tractable    correlated    invariance    gravity    stochastic    physics    equation    celebrated    axioms    navier    certain    planar    geometry    relying    models    free    velocity    euclidean    works    trap    solving    precise    deals    literature    explicit    sensitivity    seemingly    spirit    ambition    unrelated    gaussian    initiated    closely    vector    turbulent    satisfied    relation    ingredient    create    brownian    historically    once    kpz    motion    bouchaud    framework    directions    log    critical    3d    liouville    techniques    successfully    experimentally    mathematical    schramm    random    rigorously    qle    restored    conformally    circle    noise    completion    dynamics    push    plan    progress    points    conjecture    plane    combine    oscillating    flow    turbulence    conformal    exponential    emphasis    stokes    model    realistic    construction    first   

Project "LiKo" data sheet

The following table provides information about the project.


Organization address
address: BOULEVARD DU 11 NOVEMBRE 1918 NUM43
postcode: 69622

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country France [FR]
 Total cost 935˙000 €
 EC max contribution 935˙000 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2015-STG
 Funding Scheme ERC-STG
 Starting year 2016
 Duration (year-month-day) from 2016-09-01   to  2021-08-31


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 


 Project objective

This research project is organized along three seemingly unrelated directions:

(1) Mathematical Liouville gravity deals with the geometry of large random planar maps. Historically, conformal invariance was a key ingredient in the construction of Liouville gravity in the physics literature. Conformal invariance has been restored recently with an attempt of understanding large random combinatorial planar maps once conformally embedded in the plane. The geometry induced by these embeddings is conjecturally described by the exponential of a highly oscillating distribution, the Gaussian Free Field. This conjecture is part of a broader program aimed at rigorously understanding the celebrated KPZ relation. The first major goal of my project is to make significant progress towards the completion of this program. I will combine for this several tools such as Liouville Brownian motion, circle packings, QLE processes and Bouchaud trap models.

(2) Euclidean statistical physics is closely related to area (1) through the above KPZ relation. I plan to push further the analysis of critical statistical physics models successfully initiated by the works of Schramm and Smirnov. I will focus in particular on dynamics at and near critical points with a special emphasis on the so-called noise sensitivity of these systems.

(3) 3d turbulence. A more tractable ambition than solving Navier-Stokes equation is to construct explicit stochastic vector fields which combine key features of experimentally observed velocity fields. I will make the mathematical framework precise by identifying four axioms that need to be satisfied. It has been observed recently that the exponential of a certain log-correlated field, as in (1), could be used to create such a realistic velocity field. I plan to construct and analyse this challenging object by relying on techniques from (1) and (2). This would be the first genuine stochastic model of turbulent flow in the spirit of what Kolmogorov was aiming at.


year authors and title journal last update
List of publications.
2019 Christophe Garban and Hugo Vanneuville
Exceptional times for percolation under exclusion dynamics
published pages: , ISSN: 0012-9593, DOI:
Annales Scientifiques Ecole Normale Superieure 2019-07-08
2018 Christophe Garban, Nina Holden, Avelio Sepúlveda, Xin Sun
Negative moments for Gaussian multiplicative chaos on fractal sets
published pages: , ISSN: 1083-589X, DOI: 10.1214/18-ECP168
Electronic Communications in Probability 23 2019-07-08
2019 Rivera , Alejandro; Vanneuville , Hugo
Quasi-independence for nodal lines
published pages: , ISSN: 0246-0203, DOI: 1 2019-07-08
2018 Juhan Aru, Avelio Sepúlveda
Two-valued local sets of the 2D continuum Gaussian free field: connectivity, labels, and induced metrics
published pages: , ISSN: 1083-6489, DOI: 10.1214/18-EJP182
Electronic Journal of Probability 23/0 2019-07-08
2018 Christophe Garban and Hao Wu
On the convergence of FK-Ising Percolation to SLE(16/3,16/3−6)
published pages: , ISSN: , DOI:
2017 Rivera , Alejandro; Vanneuville , Hugo
The critical threshold for Bargmann-Fock percolation
published pages: , ISSN: , DOI: 1 2019-07-08
2017 Laurent Chevillard, Christophe Garban, remi Rhodes, Vincent Vargas
On a skewed and multifractal uni-dimensional random field, as a probabilistic representation of Kolmogorov\'s views on turbulence
published pages: , ISSN: , DOI:
2018 Aru, Juhan; Powell, Ellen; Sepúlveda, Avelio
Critical Liouville measure as a limit of subcritical measures
published pages: , ISSN: , DOI:
10 2019-05-27
2018 Garban, Christophe
Dynamical Liouville
published pages: , ISSN: , DOI:
2016 Rodrigo M. Pereira, Christophe Garban, Laurent Chevillard
A dissipative random velocity field for fully developed fluid turbulence
published pages: 369-408, ISSN: 0022-1120, DOI: 10.1017/jfm.2016.166
Journal of Fluid Mechanics 794 2019-06-06
2018 Muirhead, Stephen; Vanneuville, Hugo
The sharp phase transition for level set percolation of smooth planar Gaussian fields
published pages: , ISSN: , DOI:
2018 Garban, Christophe
Inverted orbits of exclusion processes, diffuse-extensive-amenability and (non-?)amenability of the interval exchanges
published pages: , ISSN: , DOI:
2018 Vanneuville, Hugo
Quantitative quenched Voronoi percolation and applications
published pages: , ISSN: , DOI:

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