Málstofa í stærðfræði ÞRIÐJUDAGINN 14. febrúar: Sigurður Örn Stefánsson

[Stefán Valdimarsson]

Athugið að þetta misseri verða málstofur almennt á þriðjudögum kl. 15:00

Dagsetning: Þriðjudagur 14. febrúar 2012 kl 3.

Staður: VRII herbergi 155.

Fyrirlesari: Sigurður Örn Stefánsson, Nordita

Titill: Growing, Markov-branching trees

Ágrip:
I will discuss a model of randomly growing, finite trees where in each
discrete timestep, one new vertex is added according to the following
growth rule: (i) An edge is selected randomly and a new vertex is
grafted onto it, dividing it into two edges or (ii) a vertex is
selected randomly and a new vertex is linked to it. When appropriate
 probability weights are assigned to these transitions, the model has a
property called Markov-branching which crudely means that a subtree of
size n is distributed in the same way as the whole tree when it had
size n. I will show how one can use the Markov-branching property to
prove that the measures generated by the growth process converge
weakly to a measure on the set of infinite trees. Furthermore, I will show that
 typically the volume of a graph ball of radius R in the infinite trees
grows with a power law R^A and that the full range of exponents A can
be obtained.

The talk is based on the paper http://arxiv.org/pdf/1103.3445.