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2021 | OriginalPaper | Buchkapitel

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

verfasst von : Sergey Foss, Alexander Sakhanenko

Erschienen in: In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius

Verlag: Springer International Publishing

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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).

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Titel: Structural Properties of Conditioned Random Walks on Integer Lattices with Random Local Constraints
verfasst von: Sergey Foss
Alexander Sakhanenko
Verlag: Springer International Publishing
Buch: In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius
Print ISBN: 978-3-030-60753-1

Electronic ISBN: 978-3-030-60754-8

Copyright-Jahr: 2021
DOI: https://doi.org/10.1007/978-3-030-60754-8_19