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2006 The probability of escaping interference
F. B. Knight, J. L. Steichen
Illinois J. Math. 50(1-4): 689-699 (2006). DOI: 10.1215/ijm/1258059488


Consider two independent sequences of travelers arriving at opposite ends of a one-lane shared pathway. Each traveler attempts to traverse the entire pathway to the opposite end. An attempt fails if the traveler collides with an opposing traveler. In a collision, both opposing travelers are annihilated. We study the probability that a traveler manages to traverse the entire length of the one-lane shared pathway unobstructed. The dynamics of the travelers include the possibility of acting as bodyguards and "running interference" for a more recent arrival traveling in the same direction. This model was developed to address some questions in the theory of crystal growth. It may have possible applications in Particle Physics as well as to traffic at a one-lane bridge. This paper develops some properties of the model while focusing on the probability that a traveler crosses the entire pathway without interference.


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F. B. Knight. J. L. Steichen. "The probability of escaping interference." Illinois J. Math. 50 (1-4) 689 - 699, 2006.


Published: 2006
First available in Project Euclid: 12 November 2009

zbMATH: 1098.60039
MathSciNet: MR2247842
Digital Object Identifier: 10.1215/ijm/1258059488

Primary: 60G35
Secondary: 60G55, 60J75, 60K40

Rights: Copyright © 2006 University of Illinois at Urbana-Champaign


Vol.50 • No. 1-4 • 2006
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