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Pathwise methods and stochastic calculus in the path towards understanding high...

Pathwise methods and stochastic calculus in the path towards understanding high dimensional phenomena 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 trans... see more

30/06/2024

WEIZMANN

1M€

Project Budget: 1M€

Project leader

WEIZMANN INSTITUTE OF SCIENCE No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

PARTICIPATION DEPralty Sin fecha límite de participación.

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Financing granted El organismo H2020 notifico la concesión del proyecto The day 2024-06-30

ERC-2018-STG: ERC Starting Grant Scope:Objectives

I+D

Cerrada does 7 years

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characteristics of the participant

Este proyecto no cuenta con búsquedas de partenariado abiertas en este momento.

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2 Participantes

WEIZMANN

1.31M€ | Leader

Química del Cinca

252.36K€ | participant

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Project duration: 70 months Date Start: 2018-08-20
End date: 2024-06-30

Project leader

WEIZMANN INSTITUTE OF SCIENCE No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Project Budget 1M€

participation deadline Sin fecha límite de participación.

Project description 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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