PhD ceremony: Mr. V. Ermolaev, 16.15 uur, Aula Academiegebouw, Broerstraat 5, Groningen
Dissertation: Gibbsian properties: examples of failures and an application
Promotor(s): prof. C. Külske, prof. A.C.D. van Enter en prof. E. Verbitsky
Faculty: Mathematics and Natural Sciences
The present thesis investigates further under which conditions the transformation of the originally Gibbs system preserves or loses its Gibbs property. This question is addressed for systems living on a complete graph or a tree. The former type of system is referred to as a mean-field system. In either case we consider Bernoulli random variables (spins) at nodes of the graph taking either +1 or -1 values. The transformations of interest are simple spin-flip dynamics altering value of each of the spins to an opposite one. For tree models we discuss different mechanisms leading to non-Gibbsianness revealing previously not discovered type of non-Gibbsianness, when any configuration within a finite region is a discontinuity point. This result underlines the importance of the size of a boundary of a finite region, this is to be contrasted with similar models living on lattices. Further we draw attention to a mean-field model in vanishing external magnetic field. In this case there are two governing parameters: the initial temperature of the system and the temperature of the dynamics. The relative simplicity of the problem allows to decompose the ‘time x initial temperature’ plane at fixed dynamical temperature into regions where conditional distributions have discontinuities and where they do not.
Finally, the last part standing relatively apart from the main topic discusses connection between variable length Markov chains and Gibbs measures. We apply the Gibbs formalism for classification problems (where VLMC were of great use) and see the superiority of the Gibbsian approach.
Thursday 26 March saw the announcement that Jacquelien Scherpen, Professor of Systems and Control Engineering at the University of Groningen, has been appointed as the Captain of Science in the High-Tech Systems and Materials (HTSM) top sector. Prof...
E-bikes, school children on bikes and the elderly in traffic. Professor of Traffic Psychology Karel Brookhuis (himself almost 70) has clear opinions on the subject. Now approaching the end of a long career, he is cautiously stepping down from his soapbox...
The new In Science podcast is all about the coronavirus.
Our guest is Casper Albers, professor in Applied Statistics and Data Visualisation.