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.
Mots clés : spider walk, recurrence, transience, rate of escape
@article{PS_2011__15__390_0, author = {Gallesco, Christophe and M\"uller, Sebastian and Popov, Serguei}, title = {A note on spider walks}, journal = {ESAIM: Probability and Statistics}, pages = {390--401}, publisher = {EDP-Sciences}, volume = {15}, year = {2011}, doi = {10.1051/ps/2010008}, mrnumber = {2870522}, zbl = {1263.60071}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ps/2010008/} }
TY - JOUR AU - Gallesco, Christophe AU - Müller, Sebastian AU - Popov, Serguei TI - A note on spider walks JO - ESAIM: Probability and Statistics PY - 2011 SP - 390 EP - 401 VL - 15 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2010008/ DO - 10.1051/ps/2010008 LA - en ID - PS_2011__15__390_0 ER -
Gallesco, Christophe; Müller, Sebastian; Popov, Serguei. A note on spider walks. ESAIM: Probability and Statistics, Tome 15 (2011), pp. 390-401. doi : 10.1051/ps/2010008. http://www.numdam.org/articles/10.1051/ps/2010008/
[1] Molecular spiders in one dimension. J. Stat. Mech. (2007). | MR
, and ,[2] Topics in the constructive theory of countable Markov chains. Cambridge University Press, Cambridge (1995). | MR | Zbl
, and ,[3] Spiders in random environment. arXiv:1001.2533 (2010). | Zbl
, , and ,[4] Rough isometries and the parabolicity of Riemannian manifolds. J. Math. Soc. Jpn 38 (1986) 227-238. | MR | Zbl
,[5] Denumerable Markov Chains. Graduate Text in Mathematics 40, 2nd edition, Springer Verlag (1976). | MR | Zbl
, and ,[6] Criterion for the recurrence or transience of stochastic process. I. J. Math. Anal. Appl. 1 (1960) 314-330. | MR | Zbl
,[7] Probability on Trees and Networks. Cambridge University Press. In preparation. Current version available at http://mypage.iu.edu/ rdlyons/, (2009).
and ,[8] Random walks on infinite graphs and groups, Cambridge Tracts in Mathematics 138. Cambridge University Press, Cambridge (2000). | MR | Zbl
,[9] Denumerable Markov chains. EMS Textbooks in Mathematics, European Mathematical Society (EMS), Zürich (2009). | MR | Zbl
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