The five nodes (Bristol, Leiden, Warwick, Zürich universities and Technion Haifa) are worldwide leading research centres in the mathematical and physical sciences. The leading senior scientists, formally representing their institutions and coordinating the research in each and across the nodes have a track record with substantial lists of publications in leading journals, plenary talks at prestigious international meetings, and supervision of postgraduate research as well as organizational expertise. We list the scientific strength of the various nodes. Bristol: spectral analysis and variational calculus (van den Berg), probability and statistical physics (Tóth); Leiden: large deviations and variational calculus (den Hollander); Warwick: random loop representations (Ueltschi); Zürich: random walks, large deviations (Bolthausen); Haifa: mathematical physics, large deviations (Ioffe). Besides the scientists named above, at each node there are a considerable number of heavy weight senior researchers and younger colleagues who will take part in the project.

School of Mathematics, University of Bristol

The School of Mathematics at Bristol is a leading centre for mathematical research. In the 2008 Research Assessment Exercise, all research groups within the school were ranked between 3rd and 5th places in the UK. Bristol will be the main node of the Network. Professors van den Berg and Toth (PI) are senior scientists, well known for their research in spectral and geometric analysis, respectively, probability theory and stochastic processes. Their research collaboration dates back to the early nineties. Both have produced important and much cited results in the topics of the present project proposal.

Technion, Israel Institute of Technology

Colleagues from Technion – Israel Institute of Technology will provide expertise in various aspects of analysis and mathematical physics. In particular: Dmitry Ioffe and Ross Pinsky are leading experts in mathematical statistical physics, respectively, analysis and stochastic processes. We also plan to attract mathematicians from other Israeli universities and research centres (in particular the Hebrew University of Jerusalem, Tel Aviv University and the Weizmann Institute). The plan is that the Technion Haifa will act as the Israeli node for the proposed network.

Institute of Mathematics, University of Leiden

Colleagues from Leiden University will provide expertise in analysis, stochastic processes and mathematical physics. In particular: Frank den Hollander is worldwide leading expert in large deviation theory. We also plan to attract mathematicians from other Dutch universities and research centres (in particular the University of Utrecht, TU Delft, TU Eindhoven and CWI Amsterdam). Leiden University will act as the Dutch node for the proposed network.

Mathematics Institute, University of Warwick

Colleagues from the Mathematics Institute in Warwick will provide expertise in mathematical physics, probability theory and analysis. In particular: Daniel Ueltschi and Stefan Adams are leading experts in stochastic representations of quantum systems, and large deviation techniques applied to them. Roman Kotecky has given shape to the modern mathematical theory of statistical physics, and critical phenomena. We intend to attract other colleagues from this node, working on related fields of mathematics

Institute of Mathematics, University of Zürich

Colleagues from the Institute of Mathematics at University of Zurich will provide expertise in various aspects of stochastic mathematics applied to the models considered. In particular: Erwin Bolthausen and his group are worldwide leading figures in random processes with interactions, large deviations, and mathematical statistical physics. Also: we plan to attract mathematicians from other Swiss universities (in particular ETH Zurich and University of Geneva). The plan is that the Institute of Mathematics, University of Zurich will act as the Swiss node for the proposed network.