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

Weakly self-avoiding walk (WSAW) is a model of simple random walk paths thatpenalizes self-intersections. On $\mathbb{Z}$, Greven and den Hollander provedin 1993 that the discrete-time weakly self-avoiding walk has an asymptoticallydeterministic escape speed, and they conjectured that this speed should bestrictly increasing in the repelling strength parameter. We study acontinuous-time version of the model, give a different existence proof for thespeed, and prove the speed to be strictly increasing. The proof uses asupersymmetric version of BFS--Dynkin isomorphism theorem, spectral theory,Tauberian theory, and stochastic dominance.

Continuous-time weakly self-avoiding walk on $\mathbb{Z}$ has strictly monotone escape speed