Structural Properties of Conditioned Random Walks on Integer Lattices with Random Local Constraints

Sergey Foss, Alexander Sakhanenko

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)peer-review

1 Citation (Scopus)


We consider a random walk on a multidimensional integer lattice with random bounds on local times, conditioned on the event that it hits a high level before its death. We introduce an auxiliary “core” process that has a regenerative structure and plays a key role in our analysis. We obtain a number of representations for the distribution of the random walk in terms of the similar distribution of the “core” process. Based on that, we prove a number of limiting results by letting the high level to tend to infinity. In particular, we generalise results for a simple symmetric one-dimensional random walk obtained earlier in the paper by Benjamini and Berestycki (J Eur Math Soc 12(4):819–854, 2010).
Original languageEnglish
Title of host publicationIn and Out of Equilibrium 3
Subtitle of host publicationCelebrating Vladas Sidoravicius
EditorsM. E. Vares, R. Fernández, L. R. Fontes , C. M. Newman
Number of pages32
ISBN (Electronic)9783030607548
ISBN (Print)9783030607531
Publication statusPublished - 2021

Publication series

NameProgress in Probability
ISSN (Print)1050-6977
ISSN (Electronic)2297-0428


  • Bounded local times
  • Conditioned random walk
  • Potential regeneration
  • Regenerative sequence
  • Separating levels
  • Skip-free distributions

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics
  • Mathematical Physics
  • Mathematics (miscellaneous)


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