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Necklace processes via Pólya urns. (English) Zbl 1160.60303
Summary: C. Mallows and L. Shepp [J. Appl. Probab. 45, No. 1, 271–278 (2008; Zbl 1213.60027)] 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 Pólya 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.
Reviewer: Reviewer (Berlin)

MSC:
60C05 Combinatorial probability
60F05 Central limit and other weak theorems
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