Bounds on the speed and on regeneration times for certain processes on regular trees
AbstractWe develop a technique that provides a lower bound on the speed of transient random walk in a random environment on regular trees. A refinement of this technique yields upper bounds on the first regeneration level and regeneration time. In particular, a lower and upper bound on the covariance in the annealed invariance principle follows. We emphasize the fact that our methods are general and also apply in the case of once-reinforced random walk. Durrett, Kesten and Limic  prove an upper bound of the form b/(b + d) for the speed on the b-ary tree, where d is the reinforcement parameter. For d > 1 we provide a lower bound of the form g^2b/(b + d), where g is the survival probability of an associated branching process.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Department of Applied Mathematics, Università Ca' Foscari Venezia in its series Working Papers with number 192.
Length: 22 pages
Date of creation: Nov 2009
Date of revision:
Random walk in a random environment; once edge-reinforced random walk; lower bound on the speed; regeneration times; regular trees.;
Find related papers by JEL classification:
- C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
- C00 - Mathematical and Quantitative Methods - - General - - - General
This paper has been announced in the following NEP Reports:
You can help add them by filling out this form.
reading list or among the top items on IDEAS.Access and download statisticsgeneral information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Marco LiCalzi).
If references are entirely missing, you can add them using this form.