title: Erosion by a one-dimensional random walk.
abstract: We consider a model introduced by Baker et al. [Phys. Rev. E 88, 042113 (2013)] of a single lattice random walker moving on a domain of allowed sites, surrounded by blocked sites. The walker enlarges the allowed domain by eroding the boundary at its random encounters with blocked boundary sites: attempts to step onto blocked sites succeed with a given probability and convert these sites to allowed sites. The model interpolates continuously between the Pólya random walker on the one-dimensional lattice and a "blind" walker who attempts freely, but always aborts, moves to blocked sites. We obtain some exact results about the walker's location and the rate of erosion.
authors.affiliation: Department of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia.
authors.forename: Rebecca H
authors.initials: RH
authors.lastname: Chisholm
authors.affiliation: Department of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia.
authors.forename: Barry D
authors.initials: BD
authors.lastname: Hughes
authors.affiliation: Department of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia.
authors.forename: Kerry A
authors.initials: KA
authors.lastname: Landman
mesh_terms: D008962:Models, Theoretical; D009038:Motion; D011336:Probability