In December 2014 I moved to the Netherlands to start my PhD research project. I worked both in the Probability Group of Prof.dr. Frank den Hollander at the Mathematical Institute of the University of Leiden and in the Networks Theory & Econophysics Group of Prof.dr. Diego Garlaschelli at the Instituut-Lorentz for Theoretical Physics at the University of Leiden. I defended my PhD thesis in December 2018.
For systems consisting of many interacting components a detailed microscopic description is usually infeasible and must be replaced by a probabilistic description. Statistical physics deals with the definition of the most appropriate probability distribution, usually referred as ensembles. Despite the fact that many textbooks still convey the message that ensemble equivalence holds for all systems, over the last decades various examples have been found for which it breaks down. The physical reason behind ensemble nonequivalence still remains to be clarified and part of my research project is to understand the hidden mechanisms behind it. Breaking of ensemble equivalence means that different choices of ensemble lead to asymptotically different behavior. Consequently, while for applications based on ensemble equivalent models the choice of the working ensemble can be arbitrary (based on mathematical convenience), for those based on nonequivalent models the choice must be dictated by a criterion indicating which ensemble is the appropriate one. This criterion must be based on the knowledge that is available about the network, i.e., which form of constraint applies in practice. Ensembles of random graphs with constraints are used for many practical purposes, such as pattern detection and network reconstruction.
F. den Hollander, M. Mandjes, A. Roccaverde, N.J. Starreveld, arXiv:1807.07750, 2018.
A. Roccaverde, Indagationes Mathematicae, Elsevier, 2018.
D. Garlaschelli, F. den Hollander, A. Roccaverde, Journal of Statistical Physics, 1-19 pp., 2018.
F. den Hollander, M. Mandjes, A. Roccaverde, N.J. Starreveld, Electron. J. Probab. Volume 23, 2018, paper no. 12, 26 pp.
D. Garlaschelli, F. den Hollander, A. Roccaverde, Journal of Physics A: Mathematical and Theoretical, Volume 50, Number 1.
D. Garlaschelli, F. den Hollander, A. Roccaverde, Nieuw Archief voor Wiskunde 5/16, nr. 3, 2015, 207-209.
2017/2018
2016/2017
2015/2016
2018:
2017:
2016:
2015: