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The brownian web (BW), which developed from the work of Arratia and then Tóth and Werner, is a random collection of paths (with specified starting points) in one plus one dimensional space–time that arises as the scaling limit of the discrete web (DW) of coalescing simple random walks. Two recently introduced extensions of the BW, the brownian net (BN) constructed by Sun and Swart, and the dynamical brownian web (DyBW) proposed by Howitt and Warren, are (or should be) scaling limits of corresponding...
Two main approaches have been considered for modelling the dynamics of the SIS model on
complex metapopulations, i.e, networks of populations connected by migratory flows whose
configurations are described in terms of the connectivity distribution of nodes (patches)
and the conditional probabilities of connections among classes of nodes sharing the same
degree. In the first approach migration and transmission/recovery process alternate
sequentially,...
In this paper a multi-scaled diffusion-approximation theorem
is proved so as to unify various applications in wave propagation
in random media: transmission of optical modes through random
planar waveguides; time delay in scattering for the linear wave
equation; decay of the transmission coefficient for large lengths
with fixed output and phase difference in weakly nonlinear random
media.
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