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The traditional Gibrat's hypotheses were once used to model the topological fluctuations of Internet. Although it seems to reproduce the scaling relation of Internet's degree distribution, the detailed micro-dynamics have never been empirically validated. Here, we analyze the distribution of degree growth rates of the Internet for various time scales. We find that in contrast to the traditional Gibrat's assumptions, none of the degree growth rates are normally distributed, but behaves as an exponential decrease on its body and a power-law decay on its tail. Moreover, the observed growth rate distribution turns out independent of the initial degree when the time interval enlarges to a year. Our observations do not consist with the traditional Gibrat law model and suggest a more complex fluctuation mechanism underlying the evolution of Internet.

Using the "δN-formalism," we obtain the expression of the non-Gaussianity of multiple-field inflationary models with the non-trivial field-space metric. Further, we have rewritten the result by using the slow-rolling approximation.

The stochastic Anderson model in discrete or continuous space is defined for a class of non-Gaussian spacetime potentials W as solutions u to the multiplicative stochastic heat equation with diffusivity κ and inverse-temperature β. The relation with the corresponding polymer model in a random environment is given. The large time exponential behavior of u is studied via its almost sure Lyapunov exponent λ = lim_t→∞ t^-1log u(t, x), which is proved to exist, and is estimated as a function of β and κ for β²κ^-1 bounded below: positivity and nontrivial upper bounds are established, generalizing and improving existing results. In discrete space λ is of order β²/log(β²/κ) and in continuous space it is between β²(κ/β²)^H/(H+1) and β²(κ/β²)^H/(1+3H).

We consider the case of a pair of particles initially in a superposition state corresponding to a separated pair of wave packets. In contrast to a previous related work, we avoid a master equation approach and we calculate exactly the time development of this non-Gaussian state due to interaction with an arbitrary heat bath. We find that coherence decays continuously, as expected. We then investigate entanglement and find that at a finite time the system becomes separable (not entangled). Thus, we see that entanglement sudden death is also prevalent in continuous variable systems which should raise concern for the designers of entangled systems.