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Critical and supercritical percolation

Total Cost €


EC-Contrib. €






 CriSP project word cloud

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

consideration    interactions    renormalization    porosity    boolean    natural    existence    group    gives    structures    continuous    understand    phenomena    random    computer    topology    structure    physics    perturbations    continuity    discrete    exponents    critical    examples    probability    space    questions    ranging    percolation    continuously    list    notable    stability    science    answer    model    found    transition    central    derivation    progress    universality    fundamental    independent    descriptions    ideas    story    limits    models    uniformly    tools    disciplines    theory    constructive    sixty    interrelated    clean    appear    concerning    shared    statistical    community    bernoulli    functions    dimension    lattice    sharpness    incomplete    rigorous    light    of    global    theoretical    spread    initially    motivate    scaling    input    macroscopic    planar    world    geometric    turned    dimensions    mathematical    respect    microscopic    relationship    transitions    last    chemical    physical    highlights    thorough    combinatorics   

Project "CriSP" data sheet

The following table provides information about the project.


Organization address
address: Raemistrasse 101
postcode: 8092

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 Switzerland [CH]
 Total cost 1˙479˙675 €
 EC max contribution 1˙479˙675 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2019-STG
 Funding Scheme ERC-STG
 Starting year 2020
 Duration (year-month-day) from 2020-09-01   to  2025-08-31


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 


 Project objective

Percolation studies how independent random input that is spread uniformly on a lattice or in space gives rise to macroscopic structures. This model, initially introduced to understand porosity, has turned out to be central for understanding fundamental features of real-world phenomena, ranging from phase transitions in physical and chemical systems to stability of Boolean functions with respect to perturbations. Over the last sixty years, a number of important mathematical results have been obtained concerning percolation, with ideas, interactions and consequences in mathematical fields such as probability, combinatorics, complex analysis, geometric group theory, planar topology and theoretical computer science. Highlights include the rigorous derivation of a number of features that are shared with other models from statistical physics: sharpness of phase transitions, renormalization theory, existence of scaling limits and critical exponents, relationship between discrete and continuous descriptions (constructive field theory)... The story is however incomplete, as some of the most fundamental questions have not yet found a mathematical answer. Two notable examples that motivate the present research proposal are the continuity of the phase transition for Bernoulli percolation in dimension three (does the macroscopic structure appear continuously?) and the universality of planar percolation (are the macroscopic features of critical percolation in two dimensions independent of the microscopic model under consideration?). In light of very recent progress, we propose here a list of interrelated projects, with the global aim of developing new tools that should enable us to make progress towards these two open problems. The impact of this study would go beyond the percolation or statistical physics community, as we aim to provide a clean and thorough understanding of some key concepts and phenomena, that would find natural applications in other disciplines.

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