English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The self-repelling Brownian polymer model (SRBP) initiated by Durrett andRogers in [Durrett-Rogers (1992)] is the continuous space-time counterpart ofthe myopic (or 'true') self-avoiding walk model (MSAW) introduced in thephysics literature by Amit, Parisi and Peliti in [Amit-Parisi-Peliti (1983)].In both cases, a random motion in space is pushed towards domains less visitedin the past by a kind of negative gradient of the occupation time measure.  We investigate the asymptotic behaviour of SRBP in the non-recurrentdimensions. First, extending 1-dimensional results from [Tarres-Toth-Valko(2009)], we identify a natural stationary (in time) and ergodic distribution ofthe environment (essentially, smeared-out occupation time measure of theprocess), as seen from the moving particle. As main result we prove that inthree and more dimensions, in this stationary (and ergodic) regime, thedisplacement of the moving particle scales diffusively and its finitedimensional distributions converge to those of a Wiener process. This resultsettles part of the conjectures (based on non-rigorous renormalization grouparguments) in [Amit-Parisi-Peliti (1983)].  The main tool is the non-reversible version of the Kipnis--Varadhan-type CLTfor additive functionals of ergodic Markov processes and the graded sectorcondition of [Sethuraman-Varadhan-Yau (2000)].

Diffusive limit for self-repelling Brownian polymers in three and more dimensions