# A model of random merging of segments

A model of random merging of segments 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

# A model of random merging of segments

, Volume 49 (3) – Oct 15, 2013
6 pages

/lp/springer_journal/a-model-of-random-merging-of-segments-cb06fIhFDR
Publisher
Springer US
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S003294601303006X
Publisher site
See Article on Publisher Site

### 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.

### Journal

Problems of Information TransmissionSpringer Journals

Published: Oct 15, 2013

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