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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.

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

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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