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A model of random merging of segments

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Abstract

We consider a growing set U of segments with integer endpoints on a line. For every pair of adjacent segments, their union is added to U with probability q. At the beginning, U contains all segments of length from 1 to m. Let h n be the probability that the segment [a, a+n] will be created; the critical value q c (m) is defined as \(\sup \{ q|\mathop {\lim }\limits_{n \to \infty } h_n = 0\} \). Lower and upper bounds for q c (m) are obtained.

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Authors and Affiliations

  1. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

    L. G. Mityushin

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  1. L. G. Mityushin
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Correspondence to L. G. Mityushin.

Additional information

Original Russian Text © L.G. Mityushin, 2013, published in Problemy Peredachi Informatsii, 2013, Vol. 49, No. 3, pp. 105–111.

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Mityushin, L.G. A model of random merging of segments. Probl Inf Transm 49, 292–297 (2013). https://doi.org/10.1134/S003294601303006X

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  • DOI: https://doi.org/10.1134/S003294601303006X

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