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論文資訊
- 類型：已發表論文
- 日期：2017-09-05
摘要
Sample Space Reducing (SSR) processes are simple 隨機 processes that offer a new route to understand 縮放律 in path-dependent processes. Here we define a cascading process that generalises the recently defined SSR processes and is able to produce 冪次定律s with arbitrary exponents. We demonstrate analytically that the frequency distributions of states are 冪次定律s with exponents that coincide with the multiplication parameter of the cascading process. In addition, we show that imposing energy conservation in SSR cascades allows us to recover Fermi's classic result on the energy spectrum of cosmic rays, with the universal exponent -2, which is independent of the multiplication parameter of the cascade. Applications of the proposed process include fragmentation processes or directed cascading 擴散 on 網絡s,
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