# A note on spider walks

Christophe Gallesco; Sebastian Müller; Serguei Popov

ESAIM: Probability and Statistics (2012)

- Volume: 15, page 390-401
- ISSN: 1292-8100

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topGallesco, Christophe, Müller, Sebastian, and Popov, Serguei. "A note on spider walks." ESAIM: Probability and Statistics 15 (2012): 390-401. <http://eudml.org/doc/222452>.

@article{Gallesco2012,

abstract = {
Spider walks are systems of interacting particles. The particles move independently as long as their movements do not violate some given rules describing the relative position of
the particles; moves that violate the rules are not realized. The goal of this paper is to study qualitative properties, as recurrence, transience, ergodicity, and positive rate of escape of these Markov processes.
},

author = {Gallesco, Christophe, Müller, Sebastian, Popov, Serguei},

journal = {ESAIM: Probability and Statistics},

keywords = {Spider walk; recurrence; transience; rate of escape; spider walk},

language = {eng},

month = {1},

pages = {390-401},

publisher = {EDP Sciences},

title = {A note on spider walks},

url = {http://eudml.org/doc/222452},

volume = {15},

year = {2012},

}

TY - JOUR

AU - Gallesco, Christophe

AU - Müller, Sebastian

AU - Popov, Serguei

TI - A note on spider walks

JO - ESAIM: Probability and Statistics

DA - 2012/1//

PB - EDP Sciences

VL - 15

SP - 390

EP - 401

AB -
Spider walks are systems of interacting particles. The particles move independently as long as their movements do not violate some given rules describing the relative position of
the particles; moves that violate the rules are not realized. The goal of this paper is to study qualitative properties, as recurrence, transience, ergodicity, and positive rate of escape of these Markov processes.

LA - eng

KW - Spider walk; recurrence; transience; rate of escape; spider walk

UR - http://eudml.org/doc/222452

ER -

## References

top- T. Antal, P.L. Krapivsky and K. Mallick, Molecular spiders in one dimension. J. Stat. Mech. (2007).
- G. Fayolle, V.A. Malyshev and M.V. Menshikov, Topics in the constructive theory of countable Markov chains. Cambridge University Press, Cambridge (1995). Zbl0823.60053
- C. Gallesco, S. Müller, S. Popov and M. Vachkovskaia, Spiders in random environment. arXiv:1001.2533 (2010). Zbl1276.60123
- M. Kanai, Rough isometries and the parabolicity of Riemannian manifolds. J. Math. Soc. Jpn38 (1986) 227–238. Zbl0577.53031
- J.G. Kemeny, J.L. Snell and A.W. Knapp, Denumerable Markov Chains. Graduate Text in Mathematics 40, 2nd edition, Springer Verlag (1976). Zbl0149.13301
- J. Lamperti, Criterion for the recurrence or transience of stochastic process. I. J. Math. Anal. Appl.1 (1960) 314–330. Zbl0099.12901
- R. Lyons and Y. Peres, Probability on Trees and Networks. Cambridge University Press. In preparation. Current version available at rdlyons/, (2009). URIhttp://mypage.iu.edu/
- W. Woess, Random walks on infinite graphs and groups, Cambridge Tracts in Mathematics138. Cambridge University Press, Cambridge (2000).
- W. Woess, Denumerable Markov chains. EMS Textbooks in Mathematics, European Mathematical Society (EMS), Zürich (2009). Zbl1219.60001

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