Necklace Processes Via Pólya Urns

Toshio Nakata
2009 Journal of Applied Probability  
Mallows and Shepp (2008) developed the following necklace processes. Start with a necklace consisting of one white bead and one black bead, and insert, one at a time, under a deterministic rule, a white bead or a black bead between a randomly chosen adjacent pair. They studied the statistical properties of the number of white beads by investigating the nature of the moments and the expected number of gaps of given length between white beads. In this note we study the number of white beads via
more » ... lya urns and give a classification of necklace processes for some general rules. Additionally, we discuss the number of runs, i.e. the number of consecutive same color beads, instead of the number of gaps.
doi:10.1017/s0021900200005362 fatcat:m33qijq3ynaxnk3dv34eyxsvdu