[Une marche excité équilibrée]
Nous étudions le processus suivant sur . À la première visite en un site, les deux premières coordonnées effectuent un saut dʼune marche simple (2-dimensionnelle). Aux visites suivantes en ce site, ce sont les deux dernières coordonnées qui effectuent un saut de marche simple. Nous montrons que ce processus est presque sûrement transitoire. Nous discutons également des dimensions inférieures et divers généralisations et questions connexes sont proposées.
The following random process on is studied. At first visit to a site, the two first coordinates perform a (2-dimensional) simple random walk step. At further visits, it is the last two coordinates which perform a simple random walk step. We prove that this process is almost surely transient. The lower dimensional versions are discussed and various generalizations and related questions are proposed.
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@article{CRMATH_2011__349_7-8_459_0,
author = {Benjamini, Ita{\i} and Kozma, Gady and Schapira, Bruno},
title = {A balanced excited random walk},
journal = {Comptes Rendus. Math\'ematique},
pages = {459--462},
publisher = {Elsevier},
volume = {349},
number = {7-8},
year = {2011},
doi = {10.1016/j.crma.2011.02.018},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2011.02.018/}
}
TY - JOUR AU - Benjamini, Itaı AU - Kozma, Gady AU - Schapira, Bruno TI - A balanced excited random walk JO - Comptes Rendus. Mathématique PY - 2011 SP - 459 EP - 462 VL - 349 IS - 7-8 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2011.02.018/ DO - 10.1016/j.crma.2011.02.018 LA - en ID - CRMATH_2011__349_7-8_459_0 ER -
%0 Journal Article %A Benjamini, Itaı %A Kozma, Gady %A Schapira, Bruno %T A balanced excited random walk %J Comptes Rendus. Mathématique %D 2011 %P 459-462 %V 349 %N 7-8 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2011.02.018/ %R 10.1016/j.crma.2011.02.018 %G en %F CRMATH_2011__349_7-8_459_0
Benjamini, Itaı; Kozma, Gady; Schapira, Bruno. A balanced excited random walk. Comptes Rendus. Mathématique, Tome 349 (2011) no. 7-8, pp. 459-462. doi : 10.1016/j.crma.2011.02.018. http://www.numdam.org/articles/10.1016/j.crma.2011.02.018/
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