Warwick Statistical Mechanics Seminar
in the Department of Mathematics
 |
This term, all seminars take place Thursdays at 2pm, room MS.03 (Zeeman Building), unless indicated otherwise. |
 Michalis Loulakis, 17.01.2013 |
| 03.10.2024 | |
| 10.10.2024 | |
| 17.10.2024 | Natalia Cardona-Tobón (National University of Colombia) The contact process on dynamical random trees with degree dependence We investigate the contact process in the case when the underlying structure evolves dynamically as a degree-dependent dynamical percolation model. Starting with a connected locally finite base graph we initially declare edges independently open with a probability that is allowed to depend on the degree of the adjacent vertices and closed otherwise. Edges are independently updated with a rate depending on the degrees and then are again declared open and closed with the same probabilities. We are interested in the contact process, where infections are only allowed to spread via open edges. Our aim is to analyse the impact of the update speed and the probability for edges to be open on the existence of a phase transition. For a general connected locally finite graph, our first result gives sufficient conditions for the critical value for survival to be strictly positive. Furthermore, in the setting of Bienaymé-Galton-Watson trees, we show that the process survives strongly with positive probability for any infection rate if the offspring distribution has a stretched exponential tail with an exponent depending on the percolation probability and the update speed. In particular, if the offspring distribution follows a power law and the connection probability is given by a product kernel and the update speed exhibits polynomial behaviour, we provide a complete characterisation of the phase transition. This talk is based on joint work with Marcel Ortgiese (University of Bath), Marco Seiler (University of Frankfurt) and Anja Sturm (University of Göttingen). Contact: Andreas |
| 24.10.2024 | Juan Neirotti (Aston University) Legislative impeachments in a neural network society Inspired by studies of government overthrows in modern South American presidential democracies, we present an agent-based Statistical Mechanics analysis of the coordinated actions of strategic political actors within legislative chambers and the conditions that can lead to premature changes in executive leadership, such as presidential impeachments or motions of no confidence in prime ministers. The legislative actors are modeled as information-processing agents, equipped with neural networks, who express opinions on issues from the presidential agenda. We construct a Hamiltonian representing the collective cost incurred by agents for holding a particular set of opinions from a range of possible stances. Using replica methods, we explore two types of disorder: in the distribution of neural network weights and in the structure of agent interactions. The resulting phase diagram illustrates how control parameters -- loosely interpreted as indices of legislative strategic support, presidential polling popularity, and the volume of issues on the presidential agenda -- govern the system behavior. The model reveals an intermediate phase where strategic behaviors in support of or against the executive coexist, flanked by phases (characterised by a pure state) where the legislative vote aligns fully with either supporting or opposing the executive. Changes in these indices, driven by external factors, can push the system out of the coexistence phase and into the opposing pure phase, triggering a phase transition that leads to the removal of the executive through constitutional means. Using data from Brazil, we analyze presidential trajectories during the democratic period starting in 1989, showing that these trajectories align with the phase diagram in terms of whether the president was removed or remained in office. Contact: Randa |
| 31.10.2024 | Jeffrey Kuan (Texas A&M University) TBA Contact: Oleg Z. |
| 07.11.2024 | Barbara Roos (Universität Tübingen) Contact: Daniel |
| 14.11.2024 | Jakob Björnberg (University of Gothenburg/Chalmers) Dimerisation in mirror models and quantum spin chains We consider two models of random loops where we prove breaking of translational symmetry. The first is a mirror model, where the loops are formed by light rays bouncing in a labyrinth of randomly oriented mirrors. The second is a probabilistic representation of a quantum spin chain, and can be obtained as a limit of the first, for inhomogeneous mirror weights. In the terminology of quantum spins, this symmetry-breaking is called “dimerisation”. Based on joint works with K. Ryan as well as with P. Muehlbacher, B. Nachtergaele and D. Ueltschi. Contact: Daniel |
| 21.11.2024 | Harini Desiraju (University of Sydney) TBA Contact: Nikos |
| 28.11.2024 | |
| 05.12.2024 | |