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NOISE SIGNED

Noise-Sensitivity Everywhere

Total Cost €

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EC-Contrib. €

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Partnership

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 NOISE project word cloud

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

katok    noise    arises    finite    environment    permutation    iid    theory    eigenfunctions    interchange    pi    operator    certain    amenability    statistical    oacute    inputs    ell2    volume    resampling    kalai    obstacle    percolation    passage    vs    gaboriau    geometry    conjecture    boolean    f2    structures    time    fast    proving    motivated    mixing    question    babai    connecting    fk    fourier    ising    critical    notion    exchange    bits    ideas    dynamics    cycle    entropy    prove    function    striking    hypercontractivity    quantum    near    macroscopic    mixes    betti    poly    input    recast    model    mechanics    sl    outstanding    refuting    first    tiny    science    walk    influence    sensitive    proportion    universality    ways    questions    naturally    hypercube    sensitivity    transformation    iff    random    alternating    physics    group    linear    transition    structure    interval    energy       directions    groups    unpredictable    glauber    planar    says    weight    computer    models    logarithmic    perhaps    friedgut    generating    output   

Project "NOISE" data sheet

The following table provides information about the project.

Coordinator
MAGYAR TUDOMANYOS AKADEMIA RENYI ALFRED MATEMATIKAI KUTATOINTEZET 

Organization address
address: REALTANODA UTCA 13-15
city: Budapest
postcode: 1053
website: http://www.renyi.hu

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 Hungary [HU]
 Total cost 1˙386˙363 €
 EC max contribution 1˙386˙363 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2017-COG
 Funding Scheme ERC-COG
 Starting year 2018
 Duration (year-month-day) from 2018-02-01   to  2023-01-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    MAGYAR TUDOMANYOS AKADEMIA RENYI ALFRED MATEMATIKAI KUTATOINTEZET HU (Budapest) coordinator 1˙386˙363.00

Map

 Project objective

Noise-sensitivity of a Boolean function with iid random input bits means that resampling a tiny proportion of the input makes the output unpredictable. This notion arises naturally in computer science, but perhaps the most striking example comes from statistical physics, in large part due to the PI: the macroscopic geometry of planar percolation is very sensitive to noise. This can be recast in terms of Fourier analysis on the hypercube: a function is noise sensitive iff most of its Fourier weight is on 'high energy' eigenfunctions of the random walk operator.

We propose to use noise sensitivity ideas in three main directions:

(A) Address some outstanding questions in the classical case of iid inputs: universality in critical planar percolation; the Friedgut-Kalai conjecture on Fourier Entropy vs Influence; noise in First Passage Percolation.

(B) In statistical physics, a key example is the critical planar FK-Ising model, with noise being Glauber dynamics. One task is to prove noise sensitivity of the macroscopic structure. A key obstacle is that hypercontractivity of the critical dynamics is not known.

(C) Babai’s conjecture says that random walk on any finite simple group, with any generating set, mixes in time poly-logarithmic in the volume. Two key open cases are the alternating groups and the linear groups SL(n,F2). We will approach these questions by first proving fast mixing for certain macroscopic structures. For permutation groups, this is the cycle structure, and it is related to a conjecture of Tóth on the interchange process, motivated by a phase transition question in quantum mechanics.

We will apply ideas of statistical physics to group theory in other novel ways: using near-critical FK-percolation models to prove a conjecture of Gaboriau connecting the first ell2-Betti number of a group to its cost, and using random walk in random environment to prove the amenability of the interval exchange transformation group, refuting a conjecture of Katok.

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The information about "NOISE" are provided by the European Opendata Portal: CORDIS opendata.

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