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Limit theorems for processes in random media

Objective

Classical random walks (CRW) have been studied for centuries, and very detailed information is known about them. However, most of the techniques for studying CRW are based on the complete regularity and the group structure of the medium. When modeling real world phenomena, this regularity assumption rarely holds, and therefore CRW is not a sufficient model. As a result, a number of non-classical models of random walk have been suggested. These models are believed to better model actual natural processes. One of the most studied of non-classical random walk models is random walk in random environment (RWRE). In RWRE the medium ("environment") in which the process takes place is random, and the law of the random walk varies as a function of the location. RWRE can model, for instance, the motion of an electron in an alloy, the movement of enzymes along a DNA sequence and many other processes. Since the CRW methodology does not work for RWRE (and, in fact, neither for other non-classical models of random walk), new methodology needed to be developed. The purpose of this project is to contribute to the study of RWRE by improving the existing methods and by developing new ones. We will work on some of the most important problems in the field, namely convergence and rate of convergence to Brownian motion for various RWRE models (e.g. reversible, perturbative and others), trapping and slowdown for RWRE models (e.g. ballistic and perturbative), ballisticity conditions, zero-one laws, and others. The output of this project is expected to contribute significantly to the understanding of RWRE systems.

Field of science

  • /social sciences/law
  • /natural sciences/biological sciences/biochemistry/biomolecules/proteins/enzymes

Call for proposal

ERC-2009-StG
See other projects for this call

Funding Scheme

ERC-SG - ERC Starting Grant

Host institution

TECHNISCHE UNIVERSITAET MUENCHEN
Address
Arcisstrasse 21
80333 Muenchen
Germany
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 213 412,55
Principal investigator
Noam Berger (Dr.)
Administrative Contact
Ulrike Ronchetti (Ms.)

Beneficiaries (2)

TECHNISCHE UNIVERSITAET MUENCHEN
Germany
EU contribution
€ 213 412,55
Address
Arcisstrasse 21
80333 Muenchen
Activity type
Higher or Secondary Education Establishments
Principal investigator
Noam Berger (Dr.)
Administrative Contact
Ulrike Ronchetti (Ms.)
THE HEBREW UNIVERSITY OF JERUSALEM
Israel
EU contribution
€ 290 587,45
Address
Edmond J Safra Campus Givat Ram
91904 Jerusalem
Activity type
Higher or Secondary Education Establishments
Administrative Contact
Jane Turner (Ms.)