Jonathan Jordan

University of Sheffield University of Sheffield


Multiple phase transitions in non-linear urns with interacting types


Probability Seminar


2nd December 2022, 3:30 pm – 4:30 pm
Fry Building, 2.04


We investigate reinforced non-linear urns with interacting types, and show that where there are three interacting types there are phenomena which do not occur with two types. In a model with three types where the interactions between the types are symmetric, we show the existence of a double phase transition with three phases: as well as a phase with an almost sure limit where each of the three colours is equally represented and a phase with almost sure convergence to an asymmetric limit, which both occur with two types, there is also an intermediate phase where both symmetric and asymmetric limits are possible. In a model with anti symmetric interactions between the types, we show the existence of a phase where the proportions of the three colours cycle and do not converge to a limit, alongside a phase where the proportions of the three colours can converge to a limit where each of the three is equally represented. This is joint work with Marcelo Costa.






Comments are closed.
css.php