# Transient random walk in ${\mathbb{Z}}^{2}$ with stationary orientations

ESAIM: Probability and Statistics (2009)

- Volume: 13, page 417-436
- ISSN: 1292-8100

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topPène, Françoise. "Transient random walk in ${\mathbb Z}^2$ with stationary orientations." ESAIM: Probability and Statistics 13 (2009): 417-436. <http://eudml.org/doc/250665>.

@article{Pène2009,

abstract = {
In this paper, we extend a result of Campanino and Pétritis [Markov Process. Relat. Fields 9 (2003) 391–412].
We study a random walk in $\{\mathbb Z\}^2$ with random orientations.
We suppose that the orientation of the kth floor
is given by $\xi_k$, where $(\xi_k)_\{k\in\mathbb Z\}$ is
a stationary sequence of random variables.
Once the environment fixed, the random walk can go
either up or down or can stay in the present floor (but moving with
respect to its orientation).
This model was introduced by Campanino and Pétritis
in [Markov Process. Relat. Fields 9 (2003) 391–412] when
the $(\xi_k)_\{k\in\mathbb Z\}$ is a sequence of
independent identically distributed random variables.
In [Theory Probab. Appl. 52 (2007) 815–826], Guillotin-Plantard and Le Ny extend this
result to a situation where the orientations of the floors are independent
but chosen with stationary probabilities (not equal to 0
and to 1).
In the present paper, we generalize the result of [Markov Process. Relat. Fields 9 (2003) 391–412]
to some cases when $(\xi_k)_k$ is stationary. Moreover we extend slightly
a result of [Theory Probab. Appl.52 (2007) 815–826].
},

author = {Pène, Françoise},

journal = {ESAIM: Probability and Statistics},

keywords = {Transience; random walk; Markov chain; oriented graphs; stationary orientations.; transience; stationary orientations},

language = {eng},

month = {9},

pages = {417-436},

publisher = {EDP Sciences},

title = {Transient random walk in $\{\mathbb Z\}^2$ with stationary orientations},

url = {http://eudml.org/doc/250665},

volume = {13},

year = {2009},

}

TY - JOUR

AU - Pène, Françoise

TI - Transient random walk in ${\mathbb Z}^2$ with stationary orientations

JO - ESAIM: Probability and Statistics

DA - 2009/9//

PB - EDP Sciences

VL - 13

SP - 417

EP - 436

AB -
In this paper, we extend a result of Campanino and Pétritis [Markov Process. Relat. Fields 9 (2003) 391–412].
We study a random walk in ${\mathbb Z}^2$ with random orientations.
We suppose that the orientation of the kth floor
is given by $\xi_k$, where $(\xi_k)_{k\in\mathbb Z}$ is
a stationary sequence of random variables.
Once the environment fixed, the random walk can go
either up or down or can stay in the present floor (but moving with
respect to its orientation).
This model was introduced by Campanino and Pétritis
in [Markov Process. Relat. Fields 9 (2003) 391–412] when
the $(\xi_k)_{k\in\mathbb Z}$ is a sequence of
independent identically distributed random variables.
In [Theory Probab. Appl. 52 (2007) 815–826], Guillotin-Plantard and Le Ny extend this
result to a situation where the orientations of the floors are independent
but chosen with stationary probabilities (not equal to 0
and to 1).
In the present paper, we generalize the result of [Markov Process. Relat. Fields 9 (2003) 391–412]
to some cases when $(\xi_k)_k$ is stationary. Moreover we extend slightly
a result of [Theory Probab. Appl.52 (2007) 815–826].

LA - eng

KW - Transience; random walk; Markov chain; oriented graphs; stationary orientations.; transience; stationary orientations

UR - http://eudml.org/doc/250665

ER -

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