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

David S. Dean·Satya N. Majumdar
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Abstract

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 m m_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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David S. Dean, Satya N. Majumdar. 2002-05-02. Phase Transition in a Random Fragmentation Problem with Applications to Computer Science. https://doi.org/10.1088/0305-4470%2F35%2F32%2F101

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