A note on spider walks

Christophe Gallesco; Sebastian Müller; Serguei Popov

ESAIM: Probability and Statistics (2012)

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

Abstract

top
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

top

Gallesco, 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
  1. T. Antal, P.L. Krapivsky and K. Mallick, Molecular spiders in one dimension. J. Stat. Mech. (2007).  
  2. G. Fayolle, V.A. Malyshev and M.V. Menshikov, Topics in the constructive theory of countable Markov chains. Cambridge University Press, Cambridge (1995).  Zbl0823.60053
  3. C. Gallesco, S. Müller, S. Popov and M. Vachkovskaia, Spiders in random environment. arXiv:1001.2533 (2010).  Zbl1276.60123
  4. M. Kanai, Rough isometries and the parabolicity of Riemannian manifolds. J. Math. Soc. Jpn38 (1986) 227–238.  Zbl0577.53031
  5. 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
  6. J. Lamperti, Criterion for the recurrence or transience of stochastic process. I. J. Math. Anal. Appl.1 (1960) 314–330.  Zbl0099.12901
  7. 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/
  8. W. Woess, Random walks on infinite graphs and groups, Cambridge Tracts in Mathematics138. Cambridge University Press, Cambridge (2000).  
  9. W. Woess, Denumerable Markov chains. EMS Textbooks in Mathematics, European Mathematical Society (EMS), Zürich (2009).  Zbl1219.60001

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.