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OPTRASTOCH SIGNED

Optimal Transport and Stochastic Dynamics

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EC-Contrib. €

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Partnership

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Project "OPTRASTOCH" data sheet

The following table provides information about the project.

Coordinator
INSTITUTE OF SCIENCE AND TECHNOLOGY AUSTRIA 

Organization address
address: Am Campus 1
city: KLOSTERNEUBURG
postcode: 3400
website: www.ist.ac.at

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 Austria [AT]
 Project website http://www.janmaas.org/erc-grant
 Total cost 1˙074˙590 €
 EC max contribution 1˙074˙590 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2016-STG
 Funding Scheme ERC-STG
 Starting year 2017
 Duration (year-month-day) from 2017-02-01   to  2022-01-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    INSTITUTE OF SCIENCE AND TECHNOLOGY AUSTRIA AT (KLOSTERNEUBURG) coordinator 1˙074˙590.00

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 Project objective

Many important properties of stochastic processes are deeply connected with the underlying geometric structure. The crucial quantity in many applications is a lower bound on the Ricci curvature, which yields powerful applications to concentration of measure, isoperimetry, and convergence to equilibrium. Since many important processes are defined in discrete, infinite-dimensional, or singular spaces, major research activity has been devoted to developing a theory of Ricci curvature beyond the classical Riemannian setting. This led to the powerful theories of Bakry-Émery and Lott-Sturm-Villani, which have been extremely successful in the analysis of geodesic spaces and diffusion processes. Building on our recent work, we will develop a wide research program that allows us to significantly enlarge the scope of these ideas. A) Firstly, we develop a comprehensive theory of curvature-dimension for discrete spaces based on geodesic convexity of entropy functionals along discrete optimal transport. Promising first results suggest that the theory initiated by the PI provides the appropriate framework for obtaining many powerful results from geometric analysis in the discrete setting. B) Secondly, we analyse discrete stochastic dynamics using methods from optimal transport. We focus on non-reversible Markov processes, which requires a significant extension of the existing gradient flow theory, and develop new methods for proving convergence of discrete stochastic dynamics. C) Thirdly, we develop an optimal transport approach to the analysis of quantum Markov processes. We will perform a thorough investigation of noncommutative optimal transport, we aim for geometric and functional inequalities in quantum probability, and apply the results to the analysis of quantum Markov processes. The project extends the scope of optimal transport methods significantly and makes a fundamental contribution to the conceptual understanding of discrete curvature.

 Publications

year authors and title journal last update
List of publications.
2019 P. L. Ferrari, P. Ghosal, P. Nejjar
Limit law of a second class particle in TASEP with non-random initial condition
published pages: 1203-1225, ISSN: 0246-0203, DOI: 10.1214/18-aihp916
Annales de l\'Institut Henri Poincaré, Probabilités et Statistiques 55/3 2020-04-01
2020 Eric A. Carlen, Jan Maas
Non-commutative Calculus, Optimal Transport and Functional Inequalities in Dissipative Quantum Systems
published pages: 319-378, ISSN: 0022-4715, DOI: 10.1007/s10955-019-02434-w
Journal of Statistical Physics 178/2 2020-04-01
2018 Peter Nejjar
Transition to Shocks in TASEPand Decoupling of Last Passage Times
published pages: 1311, ISSN: 1980-0436, DOI: 10.30757/alea.v15-49
Latin American Journal of Probability and Mathematical Statistics 15/2 2020-03-20
2019 Matthias Erbar, Jan Maas, Melchior Wirth
On the geometry of geodesics in discrete optimal transport
published pages: , ISSN: 0944-2669, DOI: 10.1007/s00526-018-1456-1
Calculus of Variations and Partial Differential Equations 58/1 2020-03-20
2018 Dan Betea, Jérémie Bouttier, Peter Nejjar, Mirjana Vuletić
The Free Boundary Schur Process and Applications I
published pages: 3663-3742, ISSN: 1424-0637, DOI: 10.1007/s00023-018-0723-1
Annales Henri Poincaré 19/12 2020-03-20
2018 ARSENIY AKOPYAN, SERGEY AVVAKUMOV
ANY CYCLIC QUADRILATERAL CAN BE INSCRIBED IN ANY CLOSED CONVEX SMOOTH CURVE
published pages: , ISSN: 2050-5094, DOI: 10.1017/fms.2018.7
Forum of Mathematics, Sigma 6 2020-03-20

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