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

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Structural Properties of Conditioned Random Walks on Integer Lattices with Random Local Constraints. / Foss, Sergey; Sakhanenko, Alexander.

Progress in Probability. ed. / Maria Eulália Vares; Roberto Fernández; Luiz Renato Fontes; Charles M. Newman. 1. ed. Birkhauser Verlag Basel, 2021. p. 407-438 (Progress in Probability; Vol. 77).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Research › peer-review

Harvard

Foss, S & Sakhanenko, A 2021, Structural Properties of Conditioned Random Walks on Integer Lattices with Random Local Constraints. in ME Vares, R Fernández, LR Fontes & CM Newman (eds), Progress in Probability. 1 edn, Progress in Probability, vol. 77, Birkhauser Verlag Basel, pp. 407-438. https://doi.org/10.1007/978-3-030-60754-8_19

APA

Foss, S., & Sakhanenko, A. (2021). Structural Properties of Conditioned Random Walks on Integer Lattices with Random Local Constraints. In M. E. Vares, R. Fernández, L. R. Fontes, & C. M. Newman (Eds.), Progress in Probability (1 ed., pp. 407-438). (Progress in Probability; Vol. 77). Birkhauser Verlag Basel. https://doi.org/10.1007/978-3-030-60754-8_19

Vancouver

Foss S, Sakhanenko A. Structural Properties of Conditioned Random Walks on Integer Lattices with Random Local Constraints. In Vares ME, Fernández R, Fontes LR, Newman CM, editors, Progress in Probability. 1 ed. Birkhauser Verlag Basel. 2021. p. 407-438. (Progress in Probability). doi: 10.1007/978-3-030-60754-8_19

Author

Foss, Sergey ; Sakhanenko, Alexander. / Structural Properties of Conditioned Random Walks on Integer Lattices with Random Local Constraints. Progress in Probability. editor / Maria Eulália Vares ; Roberto Fernández ; Luiz Renato Fontes ; Charles M. Newman. 1. ed. Birkhauser Verlag Basel, 2021. pp. 407-438 (Progress in Probability).

BibTeX

@inbook{4bf9ecf64c9841a6b306612dfea67367,

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 = "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 = "978-3-030-60753-1",

series = "Progress in Probability",

publisher = "Birkhauser Verlag Basel",

pages = "407--438",

editor = "Vares, {Maria Eul{\'a}lia} and Roberto Fern{\'a}ndez and Fontes, {Luiz Renato} and Newman, {Charles M.}",

booktitle = "Progress in Probability",

address = "Switzerland",

edition = "1",

}

RIS

TY - CHAP

T1 - Structural Properties of Conditioned Random Walks on Integer Lattices with Random Local Constraints

AU - Foss, Sergey

AU - Sakhanenko, Alexander

PY - 2021

Y1 - 2021

N2 - 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).

AB - 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).

KW - Bounded local times

KW - Conditioned random walk

KW - Potential regeneration

KW - Regenerative sequence

KW - Separating levels

KW - Skip-free distributions

UR - http://www.scopus.com/inward/record.url?scp=85118426837&partnerID=8YFLogxK

UR - https://www.elibrary.ru/item.asp?id=47519566

UR - https://www.mendeley.com/catalogue/d16356c2-a47e-3aa8-878d-a065fab85f3e/

U2 - 10.1007/978-3-030-60754-8_19

DO - 10.1007/978-3-030-60754-8_19

M3 - Chapter

AN - SCOPUS:85118426837

SN - 978-3-030-60753-1

SN - 978-3-030-60756-2

T3 - Progress in Probability

SP - 407

EP - 438

BT - Progress in Probability

A2 - Vares, Maria Eulália

A2 - Fernández, Roberto

A2 - Fontes, Luiz Renato

A2 - Newman, Charles M.

PB - Birkhauser Verlag Basel

ER -

ID: 34598591