Illinois Journal of Mathematics

The probability of escaping interference

F. B. Knight and J. L. Steichen

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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.

Article information

Illinois J. Math., Volume 50, Number 1-4 (2006), 689-699.

First available in Project Euclid: 12 November 2009

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G35: Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx]
Secondary: 60G55: Point processes 60J75: Jump processes 60K40: Other physical applications of random processes


Knight, F. B.; Steichen, J. L. The probability of escaping interference. Illinois J. Math. 50 (2006), no. 1-4, 689--699. doi:10.1215/ijm/1258059488.

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