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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

0

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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.

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

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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