David de Boer: Random colourings of trees with constant down degree

V torek, 6. decembra ob 12. uri in 30 minut, bo v okviru seminarja za kompleksno analizo predaval David de Boer z Univerze v Amsterdamu, Nizozemska.

Title: Random colourings of trees with constant down degree.

Abstract: Denote by (T_d^n,r) the rooted tree with the root r, where each vertex has d children and the leaves are at distance exactly n from r. Fix a colouring with q colours of the leaves, and look at a random proper colouring of T_d^n that agrees with the colours we fixed on the leaves. What is the probability that the root gets colour 1 under such a proper colouring? Is it 1/q, or does it depend on the fixed colouring of the leaves? If we let the distance between the root and the leaves grow, will this tend to 1/q? After looking at this as a warm up, we will allow non proper colourings and discuss how we reformulate the problem into a dynamical system, which we analyse to obtain our result. This talk is based on joint work with Ferenc Bencs, Pjotr Buys and Guus Regts.

Predavanje bo potekalo HIBRIDNO, v predavalnici 3.06 na Jadranski 21 in preko aplikacije ZOOM:

https://uni-lj-si.zoom.us/j/94049045946?pwd=T3VxZHMvY3JlaUFlVXYrSlg0Wm5zZz09

Meeting ID: 940 4904 5946 Passcode: 723320

Vljudno vabljeni!

Vodji seminarja

Franc Forstneric in Barbara Drinovec Drnovsek