@inbook{2b93e24de81b49ae8427d3767cb443b8,

title = "Structural Properties of Conditioned Random Walks on Integer Lattices with Random Local Constraints",

abstract = "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).",

keywords = "Bounded local times, Conditioned random walk, Potential regeneration, Regenerative sequence, Separating levels, Skip-free distributions",

author = "Sergey Foss and Alexander Sakhanenko",

note = "Funding Information: Research is supported by RSF research grant No. 17-11-01173-Ext. Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.",

year = "2021",

doi = "10.1007/978-3-030-60754-8_19",

language = "English",

isbn = "9783030607531",

series = "Progress in Probability",

publisher = "Birkh{\"a}user",

pages = "407--438",

editor = "Vares, {M. E.} and R. Fern{\'a}ndez and {Fontes }, {L. R.} and {Newman }, {C. M.}",

booktitle = "In and Out of Equilibrium 3",

address = "Switzerland",

}