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2 Jul 2009: Remark 3.2. It is easily seen, using (3.3), that ξ̂ equals the extinctionprobability of a Galton–Watson process with offspring distribution. ... Notethat φS1(µ) = φ′S(µ).) Hence γ̂, the asymptotic relative size of Γn,λn/n;S,equals by (3.4)

28 Jul 2015: 21. Cycle structure of the interchange process and representation theory,N. Berestycki, G. ... Kozma, Bull. Soc. Math. France. 22. Galton–Watson trees with vanishing martingale limit, N.

28 Jul 2015: Po(λ) Galton-Watson tree. The results extend to graphs with prescribeddegree sequences, where cutoff is shown both for the simple and for thenon-backtracking random walk. ... Berestycki, G. Kozma, Bull. Soc. Math. France. 33. Galton–Watson trees with

13 Nov 2020: Consider a supercritical branching process (Zn)with one progenitor and mean family-size µ 1. ... Harry Kesten’s work in probability theory 19. 6 Branching processes. The branching process (or, as Harry liked in later years to write, the

20 Mar 2020: to the discretecase. Branching processes. The branching process (sometimes called the Galton–Watson process) is arguably the most fundamentalstochastic model for population growth. ... Stigum, A limit theorem for multidi-mensional Galton–Watson

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

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

20 Apr 2012: For background on the critical Galton Watson tree conditioned to survive, see [16]. ... Corollary 3.5. Let (Zn) be a critical Galton-Watson process with infinite variance suchthat.

15 Sep 2011: 500-509]. Asymptotic Properties of Subcritical Galton-Watson Processes [pp. 510-517]. How Many Random Digits Are Required until Given Sequences Are Obtained? ... 664-667]. Almost Sure Limit Results for the Supercritical Bellman-Harris Process [pp.

6 Jul 2023: 42. xii Contents. 3 Posterior Representations for Bayesian Context Trees 493.1 Branching process representations. ... 49. 3.1.1 The prior branching process. 503.1.2 The posterior branching process.