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

In this paper, we study spatially inhomogeneous random walks on the latticeof positive half line. Fix a positive integer $a.$ Let $C$ be the collection ofpoints at which the local times of the random walk are exactly $a.$ We give acriterion to tell whether $C$ is a finite set or not. Our result answer an openproblem proposed by E. Cs\'aki, A. F\"oldes, P. R\'ev\'esz [J. Theoret. Probab.23 (2) (2010) 624-638.]. When $a=1,$ $C$ is just the set of strong cutpointsstudied in the above mentioned paper. By a moment method, when the local driftof the walk at $i\ge 1$ is $1/i,$ we show that $2|C\cap [0,n]|/\logn\overset{\mathcal D}{\rightarrow} S$ as $n\rightarrow\infty,$ where $S$ is anexponentially distributed random variable with $P(S>t)=e^{-t},\ t>0.$

Local time of transient random walk on the lattice of positive half line