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Contenido archivado el 2024-05-29

Extreme value statistics in strongly correlated systems


This proposal concerns the statistics of rare events. Extreme value statistics (EVS) originally emerged in engineering, but have since found their niche in all branches of science because they dictate the frequency of catastrophic events (floods, earthquakes, financial breakdowns).

Therefore, EVS attract much attention at the scientific and societal level and there are plenty of outstanding unsolved problems in this field. In particular, the theory is currently mainly limited to ensembles of independent an d identically distributed random variables.

In practice, however, the relevant natural phenomena (earthquakes, frequency of floods, etc.) display large fluctuations, indicative of strongly correlated underlying dynamics. Our fundamental premise is that systems displaying large fluctuations are critical in the sense of continuous phase transitions, and thus are amenable to universality classification.

In order to explore this idea, we will examine EVS in critical systems of statistical physics with interdisciplinary ramifications, beginning with the maximal-height distribution in the one- and two-dimensional Mullins-Herring surface-growth models. Next, we will study the EVS of order parameter fluctuations in critical Ising and Potts models.

Last, we will consider EVS in non-equilibrium steady states. The end product of our analysis will be an understanding of EVS of strongly correlated systems in terms of universality classes. Finally, the proposal aims to fully develop a promising collaboration that started when Moloney made a three-month visit that to ELTE in 2003 during his PhD studies.

So fruitful was that brief collaboration that his entire PhD thesis is based around the ideas that he developed with Prof. Racz and colleagues. Through a period of mobility at ELTE, Moloney would be able to resume the successful collaboration and be part of one of the most diverse and multi-disciplinary statistical physics groups in the world.

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