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In and Out of Equilibrium 3: Celebrating Vladas SidoraviciusStructural Properties of Conditioned Random Walks on Integer Lattices with Random Local Constraints

In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius: Structural Properties of... [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).] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

In and Out of Equilibrium 3: Celebrating Vladas SidoraviciusStructural Properties of Conditioned Random Walks on Integer Lattices with Random Local Constraints

Part of the Progress in Probability Book Series (volume 77)
Editors: Vares, Maria Eulália; Fernández, Roberto; Fontes, Luiz Renato; Newman, Charles M.

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References (21)

Publisher
Springer International Publishing
Copyright
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
ISBN
978-3-030-60753-1
Pages
407 –438
DOI
10.1007/978-3-030-60754-8_19
Publisher site
See Chapter on Publisher Site

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).]

Published: Nov 4, 2020

Keywords: Conditioned random walk; Bounded local times; Regenerative sequence; Potential regeneration; Separating levels; Skip-free distributions; 60K15; 60K37; 60F99; 60G99

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