Extreme Value Statistics in Mathematics, Physics and Beyond

Description and Aim

The goal of the workshop is to bring together researchers from different backgrounds to discuss fundamental properties of extrema of strongly correlated random variables and their applications in mathematics, physics, astronomy, finance and climatology. The workshop aims to facilitate exchange of ideas and techniques at interfaces, and to identify common challenges.

The following topics will be covered:

(1) Extreme value and record statistics of fractional Brownian motion.

(2) Extreme distributions in nature.

(3) Extreme value statistics and theory of random matrices and operators.

(4) Extreme distributions on partitions.

(5) Models of stochastic growth and extreme values.

Topic 1 deals with functionals of extrema of Brownian motion, Brownian excursion and Brownian meander, their higher-dimensional analogues (like the Gaussian Free Field), 1/f noise, and statistics of record-breaking events in sequences of time-dependent and strongly correlated random variables. Key applications are in climatology and financial mathematics, as well as in mesoscopic physics.

Topic 2 addresses large fluctuations in natural phenomena (such as frequency of floods and earthquakes), coming from a strongly correlated dynamics in the background. The basic premise is that systems displaying large fluctuations are critical, in the sense of second order phase transitions, so that universality concepts can be used. A key application is the study of luminosities of galaxies.

Topic 3 includes the Bethe Ansatz in sequence matching problems and its relation to the Tracy-Widom distribution, as well as conditional distributions of largest eigenvalues in different random matrix ensembles and stability criteria of dynamical systems. A key application is the study of interfacesin disordered systems.

Topic 4 focusses on integer partitions in Bose condensates, including the question how Bose-Einstein condensation manifests itself in the statistics of the maximal cycle length. In addition, multidimensional asymmetric ballistic deposition and statistics of multidimensional Young tableaux are addressed. A key application is the study of stationary probability measures on stochastic networks.

Topic 5 is devoted to a problem of practical as well as fundamental importance: the growth of aggregates by sequential stochastic deposition of elementary units. In the simplest setting, sticky particles follow trajectories in space and adhere sequentially to a growing pile. A few prominent models are: Kardar-Parisi-Zhang, Edwards-Wilkinson, Restricted Solid-on-Solid, Eden.

Apart from 35 minute lectures, the program will also include panel discussions in each of the 5 topics, as well as a round table on hot topics in extreme value statistics.