A note on spider walks

Christophe Gallesco; Sebastian Müller; Serguei Popov

ESAIM: Probability and Statistics (2011)

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

Abstract

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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.

How to cite

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Gallesco, Christophe, Müller, Sebastian, and Popov, Serguei. "A note on spider walks." ESAIM: Probability and Statistics 15 (2011): 390-401. <http://eudml.org/doc/277153>.

@article{Gallesco2011,
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},
language = {eng},
pages = {390-401},
publisher = {EDP-Sciences},
title = {A note on spider walks},
url = {http://eudml.org/doc/277153},
volume = {15},
year = {2011},
}

TY - JOUR
AU - Gallesco, Christophe
AU - Müller, Sebastian
AU - Popov, Serguei
TI - A note on spider walks
JO - ESAIM: Probability and Statistics
PY - 2011
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
UR - http://eudml.org/doc/277153
ER -

References

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  1. [1] T. Antal, P.L. Krapivsky and K. Mallick, Molecular spiders in one dimension. J. Stat. Mech. (2007). MR2338265
  2. [2] G. Fayolle, V.A. Malyshev and M.V. Menshikov, Topics in the constructive theory of countable Markov chains. Cambridge University Press, Cambridge (1995). Zbl0823.60053MR1331145
  3. [3] C. Gallesco, S. Müller, S. Popov and M. Vachkovskaia, Spiders in random environment. arXiv:1001.2533 (2010). Zbl1276.60123
  4. [4] M. Kanai, Rough isometries and the parabolicity of Riemannian manifolds. J. Math. Soc. Jpn38 (1986) 227–238. Zbl0577.53031MR833199
  5. [5] J.G. Kemeny, J.L. Snell and A.W. Knapp, Denumerable Markov Chains. Graduate Text in Mathematics 40, 2nd edition, Springer Verlag (1976). Zbl0348.60090MR407981
  6. [6] J. Lamperti, Criterion for the recurrence or transience of stochastic process. I. J. Math. Anal. Appl.1 (1960) 314–330. Zbl0099.12901MR126872
  7. [7] R. Lyons and Y. Peres, Probability on Trees and Networks. Cambridge University Press. In preparation. Current version available at http://mypage.iu.edu/ rdlyons/, (2009). 
  8. [8] W. Woess, Random walks on infinite graphs and groups, Cambridge Tracts in Mathematics 138. Cambridge University Press, Cambridge (2000). Zbl0951.60002MR1743100
  9. [9] W. Woess, Denumerable Markov chains. EMS Textbooks in Mathematics, European Mathematical Society (EMS), Zürich (2009). Zbl1219.60001MR2548569

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