Beyond the Gibbs Paradigm

Wioletta Ruszel obtained her Ph.D. degree in mathematics from the University of Groningen (The Netherlands) under the supervision of Prof. A.C.D. van Enter in September 2010. From October 2010 until October 2012 she was appointed as an Assistant professor at Technical University Eindhoven and University of Nijmegen. Since November 2012 she is working in the applied probability group at Delft University of Technology where she received the prestigious Delft fellowship for female scientists. Ruszels area of specialty evolves around interacting particle systems. In her thesis she focussed mainly on Gibbsian and non-Gibbsian properties of continuous spin systems. After her Ph.D. she broadened her area of expertise and expanded her research to particle systems on random structures such as sandpile models on random trees, Polya urn models on graphs and synchronization phenomena. She co-authored 12 publications in her area, most of them about Gibbs-non Gibbs transitions for interacting particle systems. At national and international conferences Ruszel gives regularly talks about her work and acts as a reviewer for several journals. Aernout van Enter received his Ph D degree in theoretical physics at the University of Groningen in 1981. Afterwards, he worked at the University of Heidelberg in the Institute for Applied Mathematics, supported by a Sonderforschungsbereich, at the Technion Haifa in the Physics Department, supported by a Lady Davis fellowship, and at the University of Texas at Austin in the Mathematics Department before returning to the University of Groningen, first supported by a fellowship of the Royal Dutch Academy of Sciences, and afterwards as a member of the permanent staff. He first worked in the Institute for Theoretical Physics and since ten years in the Johann Bernoulli Institute for Mathematics and Computer Science where he is a honorary professor. He has spent time for research visits at the IHES in Bures, at the Dublin Institute for Advanced Studies, and at the University of California at Irvine. He is a mathematical physicist, whose main interest is in rigorous classical statistical mechanics. He has worked on phase transition theory, on the theory of Gibbs measures and its limitations, on spin glasses, on aperiodic systems and on bootstrap percolation. Van Enter is one of the founding fathers of the notion of non-Gibbs measures. He has published almost 100 research papers, and given many lectures all over the world. He has co-organised a number of research meetings and a Les Houches summer school, is on the editorial board of some leading journals, and is active a a referee for a variety of physics and mathematics journals.

Motivation: why going beyond Gibbs measures. History. Reviewing the Gibbs measure formalism. Transformations of Gibbs measures. Decimation of Gibbs measures. Projections. Time-evolution of Gibbs measures. Local coarse-graining. A quantum excursion. Disorder and Gibbs-non-Gibbs problems. Spin models. Random walks in random environments. Further examples. Random-cluster models. Applications: Denoising algorithms and Gibbs measures. Dobrushin’s restoration program. Weakly Gibbs measures. Almost Gibbs measures, intuitively weak Gibbs measures. Conclusions.