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  2. Inhomogeneous Financial Networks and Contagious Links∗ Hamed Amini†…

    https://api.newton.ac.uk/website/v0/events/preprints/NI14089
    sr}. Given i [r] let Xi(resp. Xi ) denote the Galton-Watson process starting at a particle of type si such that thenumber of children of type sk S of a ... β̂f). Remark 16 (Branching process approximation). Consider the multi-type Galton-Watson.
  3. On the critical probability in percolation Svante Janson∗ and ...

    https://api.newton.ac.uk/website/v0/events/preprints/NI16048
    Indeed, in the subcritical phasewe expect that C(v) closely mimics a subcritical branching process, which suggests that typically |C1| (χG(p)). ... We start by recalling some well-known branching processes results (we include proofs for
  4. Sparse random graphs with clustering Béla Bollobás∗†‡ Svante…

    https://api.newton.ac.uk/website/v0/events/preprints/NI08030
    It is tempting to think that the result is‘obvious’, and indeed that a corresponding result should hold for any Galton–Watson process. ... Consider the ‘forward process’ given by ignoring backward children.This is simply a Poisson

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