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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.

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

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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