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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Zero-range processes with decreasing jump rates are known to exhibitcondensation, where a finite fraction of all particles concentrates on a singlelattice site when the total density exceeds a critical value. We study such aprocess on a one-dimensional lattice with periodic boundary conditions in thethermodynamic limit with fixed, super-critical particle density. We show thatthe process exhibits metastability with respect to the condensate location,i.e. the suitably accelerated process of the rescaled location converges to alimiting Markov process on the unit torus. This process has stationary,independent increments and the rates are characterized by the scaling limit ofcapacities of a single random walker on the lattice. Our result extendsprevious work for fixed lattices and diverging density in [J. Beltran, C.Landim, Probab. Theory Related Fields, 152(3-4):781-807, 2012], and we followthe martingale approach developed there and in subsequent publications. Besidesadditional technical difficulties in estimating error bounds for transitionrates, the thermodynamic limit requires new estimates for equilibration towardsa suitably defined distribution in metastable wells, corresponding to a typicalset of configurations with a particular condensate location. The total exitrates from individual wells turn out to diverge in the limit, which requires anintermediate regularization step using the symmetries of the process and theregularity of the limit generator. Another important novel contribution is acoupling construction to provide a uniform bound on the exit rates frommetastable wells, which is of a general nature and can be adapted to othermodels.

Metastability in a condensing zero-range process in the thermodynamic limit