Galton-Watson tree and branching loops. (English) Zbl 1078.60067

Leandre, Remi

Mladenov, Ivaïlo M.(ed.) et al., Proceedings of the 6th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 3–10, 2004. Sofia: Bulgarian Academy of Sciences (ISBN 954-84952-9-5/pbk). 276-283 (2005).

The paper starts with a survey of related works. In the second part, the author recalls a construction of the branching mechanism of a loop in two loops in a \(1+1\)-dimensional theory. Then by using a binary Galton-Watson process, the author iterates the branching mechanism and obtains a random tree labelled by the loop space, that satisfies a certain Markov property.
For the entire collection see [Zbl 1066.53003].

Reviewer: Aleksander Iksanov (Kiev)

MSC:

60J80

Branching processes (Galton-Watson, birth-and-death, etc.)

Keywords:

branching mechanism; Galton-Watson process; loop space