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Sample Space Reducing (SSR) processes are simple stochastic processes that offer a new route to understand scaling in path-dependent processes. Here we define a cascading process that generalises the recently defined SSR processes and is able to produce power laws with arbitrary exponents. We demonstrate analytically that the frequency distributions of states are power laws 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 Fermis 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 diffusion on networks, such as rumour or epidemic spreading.
We study extreme value statistics of multiple sequences of random variables. For each sequence with N variables, independently drawn from the same distribution, the running maximum is defined as the largest variable to date. We compare the running ma
Based on Jaynes maximum entropy principle, exponential random graphs provide a family of principled models that allow the prediction of network properties as constrained by empirical data (observables). However, their use is often hindered by the deg
It has been shown recently that a specific class of path-dependent stochastic processes, which reduce their sample space as they unfold, lead to exact scaling laws in frequency and rank distributions. Such Sample Space Reducing processes (SSRP) offer
The paramagnetic-to-ferromagnetic phase transition is believed to proceed through a critical point, at which power laws and scaling invariance, associated with the existence of one diverging characteristic length scale -- the so called correlation le
A generically observed mechanism that drives the self-organization of living systems is interaction via chemical signals among the individual elements -- which may represent cells, bacteria, or even enzymes. Here we propose a novel mechanism for such