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Extreme Value Statistics in Mathematics, Physics and Beyond
The goal of the workshop was to bring together researchers from different backgrounds to discuss fundamental properties of extrema of strongly correlated random variables, to establish common features of systems of different origin, to elaborate on finding a unifying language for the description of these systems, and to discuss applications in mathematics, physics, astronomy, finance and climatology. Five core topics were included:
(1) Extreme value and record statistics of
fractional Brownian motion
A total of 40 researchers attended the workshop, including some 10 junior researchers. A total of 20 talks were presented. In addition, the program included parallel discussions in small groups on each of the five core topics, as well as a plenary round-table discussion,moderated by Aernout van Enter and Joachim Krug. Both events added a lot to the workshop, generated fruitful information and original points of view, and are recommended by the organisers as an efficient way of communication on a more strategic and exploratory level. Some of the participants expressed the opinion that it would have been better to organise the topical discussions consecutively and not in parallel.
One scientific highlight: during the workshop the central role of the Tracy-Widom distribution became all apparent. Apart from the statistics of extreme eigenvalues of random matrices, this distribution shows up in many different areas, e.g. growth models, branching processes, and random walks interacting with themselves and with their environment. The talk by Celine Nadal was particularly impressive, since her approach made the derivation of the Tracy-Widom distribution via orthogonal polynomials almost elementary. The discussions that followed, with comments by Bernard Derrida, Victor Dotsenko and Satya Majumdar, gave the participants the feeling that the universality of the Tracy-Widom distribution can finally be fully understood.
Another eye-opener was the presentation by Victor Dotsenko who, reporting on his work and related work by Calabrese, Le Doussal and Rosso, explained how the Tracy-Widom distribution emerges from the weak interaction scaling behaviour of the partition function of the directed random polymer in random environment, whose analysis has illuded researchers for over 20 years. This link also appears in the recent work by Amir, Corwin and Quastel.
The relaxed programme, typical for Lorentz Center workshops, with ample time between presentations and with office space made available for small working groups, helped much to increase the interaction. The support and the enthusiasm of the staff of the Lorentz Center was perfect. The organisers are grateful for the perfect arrangement that made this workshop into a most efficient meeting.
(Nottingham, United Kingdom)