Phase Transition in a Random Fragmentation Problem with Applications to Computer Science

Details Phase Transition in a Random Fragmentation Problem with Applications to Computer Science Phase Transition in a Random Fragmentation Problem with Applications to Computer Science

2002-05-02

arxiv.org/abs/cond-mat/0205034v1

J. Phys. A. 35, L501 (2002)

Physics

Condensed Matter

Statistical Mechanics

5 pages RevTeX, 3 figures (.eps)

Scientific paper

10.1088/0305-4470/35/32/101

We study a fragmentation problem where an initial object of size x is broken into m random pieces provided x>x_0 where x_0 is an atomic cut-off. Subsequently the fragmentation process continues for each of those daughter pieces whose sizes are bigger than x_0. The process stops when all the fragments have sizes smaller than x_0. We show that the fluctuation of the total number of splitting events, characterized by the variance, generically undergoes a nontrivial phase transition as one tunes the branching number m through a critical value m=m_c. For mm_c they are anomalously large and non-Gaussian. We apply this general result to analyze two different search algorithms in computer science.

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