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Hydrodynamic Limits and Equilibrium Fluctuations: universality from stochastic systems

Total Cost €


EC-Contrib. €






Project "HyLEF" data sheet

The following table provides information about the project.


Organization address
city: LISBOA
postcode: 1049-001

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 Portugal [PT]
 Project website
 Total cost 1˙179˙496 €
 EC max contribution 1˙179˙496 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2016-STG
 Funding Scheme ERC-STG
 Starting year 2016
 Duration (year-month-day) from 2016-12-01   to  2021-11-30


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    INSTITUTO SUPERIOR TECNICO PT (LISBOA) coordinator 1˙179˙496.00


 Project objective

A classical problem in the field of interacting particle systems (IPS) is to derive the macroscopic laws of the thermodynamical quantities of a physical system by considering an underlying microscopic dynamics which is composed of particles that move according to some prescribed stochastic, or deterministic, law. The macroscopic laws can be partial differential equations (PDE) or stochastic PDE (SPDE) depending on whether one is looking at the convergence to the mean or to the fluctuations around that mean. One of the purposes of this research project is to give a mathematically rigorous description of the derivation of SPDE from different IPS. We will focus on the derivation of the stochastic Burgers equation (SBE) and its integrated counterpart, namely, the KPZ equation, as well as their fractional versions. The KPZ equation is conjectured to be a universal SPDE describing the fluctuations of randomly growing interfaces of 1d stochastic dynamics close to a stationary state. With this study we want to characterize what is known as the KPZ universality class: the weak and strong conjectures. The latter states that there exists a universal process, namely the KPZ fixed point, which is a fixed point of the renormalization group operator of space-time scaling 1:2:3, for which the KPZ is also invariant. The former states that the fluctuations of a large class of 1d conservative microscopic dynamics are ruled by stationary solutions of the KPZ. Our goal is threefold: first, to derive the KPZ equation from general weakly asymmetric systems, showing its universality; second, to derive new SPDE, which are less studied in the literature, as the fractional KPZ from IPS which allow long jumps, the KPZ with boundary conditions from IPS in contact with reservoirs or with defects, and coupled KPZ from IPS with more than one conserved quantity. Finally, we will analyze the fluctuations of purely strong asymmetric systems, which are conjectured to be given by the KPZ fixed point.


year authors and title journal last update
List of publications.
2019 Aritra Kundu, Cédric Bernardin, Keji Saito, Anupam Kundu, Abhishek Dhar
Fractional equation description of an open anomalous heat conduction set-up
published pages: 13205, ISSN: 1742-5468, DOI: 10.1088/1742-5468/aaf630
Journal of Statistical Mechanics: Theory and Experiment 2019/1 2019-09-04
2018 L. Avena, M. Jara, F. Völlering
Explicit LDP for a slowed RW driven by a symmetric exclusion process
published pages: 865-915, ISSN: 0178-8051, DOI: 10.1007/s00440-017-0797-6
Probability Theory and Related Fields 171/3-4 2019-09-04
2019 Milton Jara, Gregorio R. Moreno Flores
Scaling of the Sasamoto-Spohn model in equilibrium
published pages: , ISSN: 1083-589X, DOI: 10.1214/18-ECP206
Electronic Communications in Probability 24/0 2019-09-04
2018 L. Avena, M. Jara, F. Völlering
Explicit LDP for a slowed RW driven by a symmetric exclusion process
published pages: 865-915, ISSN: 0178-8051, DOI: 10.1007/s00440-017-0797-6
Probability Theory and Related Fields 171/3-4 2019-06-13
2018 Patrícia Gonçalves, Milton Jara
Density fluctuations for exclusion processes with long jumps
published pages: 311-362, ISSN: 0178-8051, DOI: 10.1007/s00440-017-0758-0
Probability Theory and Related Fields 170/1-2 2019-06-13
2017 Patrícia Gonçalves, Milton Jara
Stochastic Burgers equation from long range exclusion interactions
published pages: 4029-4052, ISSN: 0304-4149, DOI: 10.1016/
Stochastic Processes and their Applications 127/12 2019-06-13
2018 Cédric Bernardin, Patrícia Gonçalves, Milton Jara, Marielle Simon
Nonlinear Perturbation of a Noisy Hamiltonian Lattice Field Model: Universality Persistence
published pages: 605-659, ISSN: 0010-3616, DOI: 10.1007/s00220-018-3191-z
Communications in Mathematical Physics 361/2 2019-06-13

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