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PATHWISE SIGNED

Pathwise methods and stochastic calculus in the path towards understanding high-dimensional phenomena

Total Cost €

0

EC-Contrib. €

0

Partnership

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 PATHWISE project word cloud

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

theory    robustness    deviations    mathematics    progress    originating    variance    kls    quantitative    hypercube    interacting    asz    behavior    dimension    works    1    particle    few    concepts    entropic    isoperimetric    hyperplane    science    convexity    thereof    space    versions    computer    brunn    geometry    distributions    adjacent    networks    conjecture    dimensional    minkowski    mean    transportation    latter    relies    stochastic    kernel    kannan    statistics    rely    jumps    heat    gaussian    inequalities    tools    free    regarding    introduction    managed    lov    corresponding    tractable    connections    limit    pathwise    hypercontractivity    nonlinear    associate    object    calculus    phenomena    probability    extend    conjectures    quantities    former    coauthors    boolean    mass    concentration    simonovits    inequality    play    convex    bounds    regularization    ideas    noise    first    gibbs    questions    symbiosis    bodies    stability    entropy    semigroup    central    notions    explore    theorems   

Project "PATHWISE" data sheet

The following table provides information about the project.

Coordinator		 WEIZMANN INSTITUTE OF SCIENCE 

Organization address
address: HERZL STREET 234
city: REHOVOT
postcode: 7610001
website: www.weizmann.ac.il

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 Israel [IL]
 Total cost 1˙308˙188 €
 EC max contribution 1˙308˙188 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2018-STG
 Funding Scheme ERC-STG
 Starting year 2019
 Duration (year-month-day) from 2019-01-01   to  2023-12-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    WEIZMANN INSTITUTE OF SCIENCE IL (REHOVOT) coordinator 1˙308˙188.00

Map

 Project objective

Concepts from the theory of high-dimensional phenomena play a role in several areas of mathematics, statistics and computer science. Many results in this theory rely on tools and ideas originating in adjacent fields, such as transportation of measure, semigroup theory and potential theory. In recent years, a new symbiosis with the theory of stochastic calculus is emerging.

In a few recent works, by developing a novel approach of pathwise analysis, my coauthors and I managed to make progress in several central high-dimensional problems. This emerging method relies on the introduction of a stochastic process which allows one to associate quantities and properties related to the high-dimensional object of interest to corresponding notions in stochastic calculus, thus making the former tractable through the analysis of the latter.

We propose to extend this approach towards several long-standing open problems in high dimensional probability and geometry. First, we aim to explore the role of convexity in concentration inequalities, focusing on three central conjectures regarding the distribution of mass on high dimensional convex bodies: the Kannan-Lov'asz-Simonovits (KLS) conjecture, the variance conjecture and the hyperplane conjecture as well as emerging connections with quantitative central limit theorems, entropic jumps and stability bounds for the Brunn-Minkowski inequality. Second, we are interested in dimension-free inequalities in Gaussian space and on the Boolean hypercube: isoperimetric and noise-stability inequalities and robustness thereof, transportation-entropy and concentration inequalities, regularization properties of the heat-kernel and L_1 versions of hypercontractivity. Finally, we are interested in developing new methods for the analysis of Gibbs distributions with a mean-field behavior, related to the new theory of nonlinear large deviations, and towards questions regarding interacting particle systems and the analysis of large networks.

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

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