Geodesic
On a structure of a conditioned random walk on the integers with bounded local times
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 1265-1278

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We consider a sample path of a random walk on the integers with bounded local times, conditioned on the event that it hits a high level. Under an auxiliary assumption, we obtain representations for its distribution in terms of the corresponding limiting sequence. Then we prove limiting results as the high level grows. In particular, we generalize results for a simple symmetric random walk obtained earlier by Benjamini and Berectycki (2010).
Keywords: random walk, bounded local times, conditioned random walk, regenerative process, potential regeneration. 
A. I. Sakhanenko; S. G. Foss. On a structure of a conditioned random walk on the integers with bounded local times. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 1265-1278. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a51/
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[1] I. Benjamini, N. Berectycki, “Random paths with bounded local time”, Journal of the European Mathematical Society, 12:4 (2010), 819–854 | DOI | MR | Zbl

[2] I. Benjamini, N. Berectycki, “An integral test for the transience of a Brownian path with limited local time”, Annales de l'Institut Henri Poincare — Probabilites et Statistiques, 47:2 (2011), 539–558 | DOI | MR | Zbl

[3] N. Berestycki, P. Moerters, N. Sidorova, A conditioning principle for Galton-Watson trees, arXiv: 1006.2315 [math.PR]

[4] M. Kolb, M. Savov, Transience and recurrence of a Brownian path with limited local time and its repulsion envelope, arXiv: 1312.4131 [math.PR] | MR