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15 Aug 2012: PERCOLATION ANDDISORDERED SYSTEMSGeorey GRIMMETT. 2PREFACEThis course aims to be a (nearly) self-contained account of part of the mathematicaltheory of percolation and related topics. The rst nine chapters summarise rigorousresults in percolation

15 Aug 2012: We consider a (Galton–Watson) branching process with family-size probabilitygenerating function G satisfying. ... Consider a multi-type (Galton–Watson) branching process with a set I of types;I may be finite or countably infinite.

15 Aug 2012: See Harris (1963)Ch. I; this book uses the more traditional name Galton–Watson process for thebranching process). ... is any Bienaymé–Galton–Watson branching process with the mean number γ of offspring per individualstrictly greater than 1, but

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)

15 Aug 2012: PERCOLATION AND. DISORDERED SYSTEMS. Geoffrey GRIMMETT. Percolation and Disordered Systems 143. PREFACE. This course aims to be a (nearly) self-contained account of part of the math-ematical theory of percolation and related topics. The first nine

13 Nov 2020: Harry Kesten’s work in probability theory 19. 6 Branching processes. The branching process (or, as Harry liked in later years to write, the Bienaymé–Galton–Watson process) is the most

18 Oct 2021: Kesten and B. P. Stigum. Additional limit theorems for in-decomposable multidimensional Galton–Watson processes. ... A limit theorem for multidimen-sional Galton–Watson processes. Ann. Math. Statist., 37:1211–1223, 1966.

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

8 Aug 2008: One might easily believe thathe accorded greater credit to the Reverend Henry William Watson for his foundingmembership of the Alpine Club than for his (incomplete) solution to the extinctionproblem for branching

14 May 2024: Search site. Statistical Laboratory. History of the Statistical Laboratory. A Realised Path. The Cambridge Statistical Laboratory upto 1993 (revised 2002). Contents. 1. 1947-55 Creation and confirmation. 1955-61 Disaster and diaspora. 1961-66 The