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in this article a multilayer parking system of size n=3 is studied. We prove that the asymptotic limit of the particle density in the center approaches a maximum of 1/2 in higher layers. This means a significant increase of capacity compared to the first layer where this value is 1/3. This is remarkable because the process is solely driven by randomness. We conjecture that the results applies to all finite parking systems with n larger or equal than 2.
In this article a multilayer parking system with screening of size n=3 is studied with a focus on the time-dependent particle density. We prove that the asymptotic limit of the particle density increases from an average density of 1/3 on the first la
Consider an infinite tree with random degrees, i.i.d. over the sites, with a prescribed probability distribution with generating function G(s). We consider the following variation of Renyis parking problem, alternatively called blocking RSA: at every
We introduce a class of stochastic processes with reinforcement consisting of a sequence of random partitions ${mathcal{P}_t}_{t ge 1}$, where $mathcal{P}_t$ is a partition of ${1,2,dots, Rt}$. At each time~$t$,~$R$ numbers are added to the set being
The formation of high-mass stars is usually accompanied by powerful protostellar outflows. Such high-mass outflows are not simply scaled-u
Multi-layer networks or multiplex networks are generally considered as the networks that have the same set of vertices but different types of edges. Multi-layer networks are especially useful when describing the systems with several kinds of interact