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- W87510805 abstract "We consider the question of existence of a unique invariant probability distribution which satisfies some evolutionary property. The problem arises from the random graph theory but to answer it we treat it as a dynamical system in the functional space, where we look for a global attractor. We consider the following bifurcation problem: Given a probability measure $mu$, which corresponds to the weight distribution of a link of a random graph we form a positive linear operator $Phi$ (convolution) on distribution functions and then we analyze a family of its exponents with a parameter $lambda$ which corresponds to connectivity of a sparse random graph. We prove that for every measure $mu$ (emph{i.e.}, convolution $Phi$) and every $lambda< e$ there exists a unique globally attracting fixed point of the operator, which yields the existence and uniqueness of the limit probability distribution on the random graph. This estimate was established earlier cite{KarpSipser} for deterministic weight distributions (Dirac measures $mu$) and is known as $e$-cutoff phenomena, as for such distributions and $lambda>e$ there is no fixed point attractor. We thus establish this phenomenon in a much more general sense." @default.
- W87510805 created "2016-06-24" @default.
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- W87510805 date "2004-02-21" @default.
- W87510805 modified "2023-09-27" @default.
- W87510805 title "Dynamics of exponential linear map in functional space" @default.
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