Objective Random walk in random environment (RWRE) is one of the standard models in the study of random media. Originally motivated by molecular biology applications and subsequently used in the modeling of disordered systems, it has been a constant source of fascinating mathematical phenomena and challenging open problems over the last four decades. The theory of large deviations is a cornerstone of modern probability, with applications to statistical mechanics, information theory, control engineering, risk management and many other fields.The main goal of the proposed project is to attain a clear and detailed understanding of the large deviation properties of multidimensional RWRE. The objectives can be summarized as follows: (i) Obtain simple expressions for the quenched and the averaged large deviation rate functions. (ii) Compare these rate functions and find a formula that links them. (iii) Identify the dynamics of the walk when it is conditioned to have an atypical velocity. (iv) Characterize when the new dynamics is obtained from the original one by a simple change of measure. (v) Find the ergodic invariant measure on environments from the point of view of the particle under such a conditioning.The project will build on the past accomplishments of the researcher on this topic and will involve variational formulas for the rate functions and their minimizers. The researcher will start by studying directed RWRE and focus on specific environment distributions. He will then consider general distributions and adapt the results to ballistic undirected walks by making use of regeneration times. The techniques are robust, they also cover polymers in random environments, and are likely to shed light on the open problem of strong vs. very strong disorder. The project has applications to some of the most active areas of probability theory, statistical mechanics, mathematical physics, and stochastic PDEs. Fields of science natural sciencesphysical sciencestheoretical physicsparticle physicsnatural sciencesmathematicsapplied mathematicsmathematical physicsnatural sciencesphysical sciencesclassical mechanicsstatistical mechanicsnatural sciencesmathematicsapplied mathematicsstatistics and probabilitynatural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equations Programme(s) FP7-PEOPLE - Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Topic(s) FP7-PEOPLE-2012-CIG - Marie-Curie Action: "Career Integration Grants" Call for proposal FP7-PEOPLE-2012-CIG See other projects for this call Funding Scheme MC-CIG - Support for training and career development of researcher (CIG) Coordinator KOC UNIVERSITY Address Rumeli feneri yolu sariyer 34450 Istanbul Türkiye See on map Region İstanbul İstanbul İstanbul Activity type Higher or Secondary Education Establishments Administrative Contact Askim Demiryurek (Mrs.) Links Contact the organisation Opens in new window Website Opens in new window EU contribution No data Participants (1) Sort alphabetically Sort by EU Contribution Expand all Collapse all BOGAZICI UNIVERSITESI Participation ended Türkiye EU contribution € 75 000,00 Address Bebek 34342 Istanbul See on map Region İstanbul İstanbul İstanbul Activity type Higher or Secondary Education Establishments Administrative Contact Murat Akman (Mr.) Links Contact the organisation Opens in new window Website Opens in new window Other funding No data
