A model of random merging of segments

  • Authors:

  • L. G. Mityushin

  • Affiliations:

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

  • Venue:
  • Problems of Information Transmission
  • Year:
  • 2013

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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 hn be the probability that the segment [a, a+n] will be created; the critical value qc(m) is defined as $\sup \{ q|\mathop {\lim }\limits_{n \to \infty } h_n = 0\} $. Lower and upper bounds for qc(m) are obtained.