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ERC Consolidator Grant 772466
Noise-Sensitivity Everywhere (NOISE)
Gábor Pete

Alfréd Rényi Institute of Mathematics
February 2018 - January 2023

Press release of highlighted projects by the European Research Council, including mine.

Postdoc position open now.

Mathematical summary:

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.

This project proposes to use noise sensitivity ideas in three main directions:

We will also apply ideas of statistical physics to group theory in other novel ways, such as understanding the relation between the first ell-2-Betti number of a group and its measurable cost, or using random walks in random environment to prove amenability of certain groups.

Project members:

Ábel Farkas (PostDoc 2018- Rényi)
Fractal percolation, geometric measure theory.

Pál Galicza (PhD student 2014- CEU)
Noise sensitivity of Boolean functions and percolation. Sparse reconstruction in spin systems.

Richárd Patkó (PhD student 2017- BME)
Representation theory and random walks on groups

Sándor Rokob (PhD student 2018- BME, co-advised with Balázs Ráth)
Random interlacements and Uniform Spanning Forests