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A number of practical problems, including questions about reliability of Geiger counters and short-circuits in electric cables, reduce to the mathematical problem of coincidences in Poisson patterns. This paper presents the probability of no coincidences as well as asymptotic formulas and simple bounds for that probability under a variety of circumstances. The probability of exactly N coincidences is also found in some cases.
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Gilbert et al. (1957) studied this question.
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