This workshop is the fifth in a successful series of YEP meetings at EURANDOM in the years 2004-2007. This year, the main focus of the workshop will be the investigation of the large scale behaviour of systems whose “interaction network” is modelled by random graphs.

Statistical mechanics is now more than three decades away from the introduction of disordered interactions in the case of spin glasses (Mezard, Parisi, Virasoro “Spin Glass Theory and Beyond”, 1987). Beyond its original scope of modelling certain magnetic alloys in condensed matter physics, the proposed statistical mechanics formalism has proved to be extremely useful to analyze problems in a variety of areas as diverse as combinatorial optimisation and neural networks, with applications to biological, economical and social sciences. The rich mathematical structure of spin glasses is nowadays a leading research topic in probability theory (M. Talagrand, “Spin glasses: a challenge to mathematicians”, 2003) and it can be seen as a first attempt to introduce randomness in an interacting system. Recently, diluted spin glasses have moved the theory forward, adding a new source of randomness in the connectivity property of the interaction network, like those of Erdiös-Rényi random graphs. They are also relevant in computer science, since many random optimization problems are mapped in a natural way into the study of ground states of diluted mean-field spin glass models (for example the K-sat model has been solved within the framework of “one-step replica symmetry breaking”).

Complex networks emerging in real systems (found in biology, social sciences, and internet and power grids) have revealed interesting properties of small world (Watts, 1999) and scale free type (Barabasi, 2002) which led to an explosive development of the mathematical theory of random graphs. The modelling of complex networks has given rise to a large number of random graphs models, in which some correlations structure is introduced in the model, for example the so-called “preferential attachment” type. The necessity to build a theory of interacting particles on random networks is a step to be naturally pursued in the near future.

The goal of the workshop would be to bring together the scholars whose interest lies in the intersection of disordered statistical mechanics and random graphs with a clear emphasis on applications.

Francesco Guerra (University Roma 1, La Sapienza): “Probabilistic aspect of spin glass theory”

Hidetoshi Nishimori (Tokyo Institute of Technology): “ Combinatorial optimization problems and quantum annealing“.

There will also be contribute talks by the participants, as well as talks by leading experts in the field:

A. Bovier (Weierstrass Institute, Berlin) R. v.d.Hofstad (Eindhoven & EURANDOM)
J. Kurchan (ESPCI , Paris, France), E. Marinari (University Roma 1, La Sapienza)
R. Zecchina (Politecnico Torino)

Selected contribution to the conference will be invited for a Special Issue of Journal of Mathematical Physics.

Prof. P. Contucci (Bologna University) - contucci@dm.unibo.it

Prof. C. Giardinà (Eindhoven University of Technology/EURANDOM) - c.giardina@tue.nl

The Organizers would like to acknowledge the following organizations for their contributions

YEP (Young European Probabilists) workshops

2004 -- 2005 -- 2006 --2007

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