Probability Theory
A balanced excited random walk
[Une marche excité équilibrée]

Présenté par : Marc Yor

Benjamini, Itaı1 ; Kozma, Gady1 ; Schapira, Bruno2
1 The Weizmann Institute of Science, Rehovot POB 76100, Israel
2 Département de Mathématiques, bâtiment 425, Université Paris-Sud 11, 91405 Orsay cedex, France
Comptes Rendus. Mathématique, Tome 349 (2011) no. 7-8, pp. 459-462.

Nous étudions le processus suivant sur Z4. 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 Z4 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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DOI : 10.1016/j.crma.2011.02.018
Benjamini, Itaı 1 ; Kozma, Gady 1 ; Schapira, Bruno 2

1 The Weizmann Institute of Science, Rehovot POB 76100, Israel
2 Département de Mathématiques, bâtiment 425, Université Paris-Sud 11, 91405 Orsay cedex, France 
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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. https://www.numdam.org/articles/10.1016/j.crma.2011.02.018/

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