Center for Interdisziplinary Research
 
 

ZiF Workshop

Complex Systems of Interacting Particles

Date: 19 - 22 May 2014

Convenors: Tobias Kuna (Reading, GBR), Oleksandr Kutovyi (Boston, USA), Michael Röckner (Bielefeld, GER)

Interacting particle systems constitute an appropriate paradigm for large sways of the real world. Therefore, any essential progress made towards understanding their complex behaviour would be deemed of great importance. Besides their applications to the real world, interacting particle systems may generically appear also in seemingly unrelated problems after thorough structural analysis. An interacting particle system consists of a large number of objects which should be reasonably enough considerable, as well as identical and localised. Each object can have influence on the other, where the influence may depend on their spatial location. Essential questions are how such systems evolve, and what their long time behaviour and their aggregated properties on large scales are. The presentations at the conference reflected this inter-disciplinary and multi-faceted characteristics of the field and gave, at the same time, perfect concrete examples highlighting the above general and abstract description of the field. The following examples are chosen merely eclectically and only the name of the presenter is indicated. Plants like trees or grass, their birth and their death as individuals are described by the Bolker-Pacala model with very different characteristic from the classical particle models motivated by soft-matter physics. By using techniques of stochastic order, stability was established (Ostap Hryniv) and the qualitative influence of spatial extensions on the long time behaviour was investigated (Jurij Kozicki). Intermittency behaviour and development of patches is related to the influence of irregular environment (Stanislav Molchanov). Such random environments and their large scale behaviour for different correlation structures are of independent mathematical interest (Carlo Boldrighini, Jean-Dominique Deuschel, Alessandro Pellegrinotti). Elena Zhizhina presented software based on the dynamics of interaction particle systems, where the particles are the pixels of an image, which automatically counts persons in images of crowds. By considering tumor cells as the elementary entities in a particle system, tumor growth was modelled (Tyll Krüger). Further areas of applications in sciences considered were genetic recombination, quantum computing, quantum systems and neuron growth. The representation theory of infinite-dimensional groups is an example of a mathematical problem which seems at first to be completely unrelated to particle systems, however their spectrum is related to a Markov dynamics for a particle system (Grigori Olshanski). Dynamical systems with fractional derivatives are naturally related as they effectively describe large scale behaviour of particle systems with memory effect (Jose Luis da Silva, Martin Grothaus, Anatoly Kochubei, Gregoriy Torbin). These talks about different areas of applications for infinite particle systems were complemented by a large number of talks given by experts in the mathematical theory of particle systems and related areas of stochastics giving the mathematical backbone to the applications. As we concentrate on the interdisciplinary aspects in this report, these contributions cannot be reported in detail, although they were an integral part of the conference. Spontaneously organised discussions gave an informal note to the meeting and were essential for its success, which was strongly enhanced by the splendid, though very unlikely, mid-summer week in May.

Participants

Sergio Albeverio (Bonn, GER), Philippe Blanchard (Bielefeld, GER), Wolfgang Bock (Lissabon, POR), Leonid Bogachev (Leeds, GBR), Carlo Boldrighini (Rom, ITA), Marcin Bodych (Wroclaw, POL), José Luis da Silva (Funchal, POR), Alex Daletskii (York, GBR), Jean-Dominique Deuschel (Berlin, GER), David Elworthy (Coventry, GBR), Gerald A. Goldin (Piscataway, USA), Alexander Grigoryan (Bielefeld, GER), Martin Grothaus (Kaiserslautern, GER), Ostap Hryniv (Durham, GBR), Anatoly Kochubei (Kiew, UKR), Vassili Kolokoltsov (Coventry, GBR), Yuri Kondratiev (Bielefeld, GER), Jurij Kozicki (Lublin, POL), Tyll Krüger (Wroclaw, POL), Eugene Lytvynov (Swansea, GBR), Ilya Molchanov (Bern, SUI), Stanislav Molchanov (Charlotte, USA), Maria João Oliveira (Lissabon, POR), Grigori Olshanski (Moskau, RUS), Tomasz Ozanski (Wroclaw, POL), Leonid Pastur (Kharkov, UKR), Tetyana Pasurek (Bielefeld, GER), Robert I.A. Patterson (Berlin, GER), Alessandro Pellegrinotti (Rom, ITA), Sergey Pirogov (Moskau, RUS), Mario Pulvirenti (Rom, ITA), Sylvie Roelly (Potsdam, GER), Senya Shlosman (Marseille, FRA), Gregoriy Torbin (Kiew, UKR), Livio Triolo (Rom, ITA), Anatoly Vershik (St. Petersburg, RUS), Rui Vilela Mendes (Lissabon, POR), Valentin Zagrebnov (Marseille, FRA), Hans Zessin (Berlin, GER), Elena Zhizhina (Moskau, RUS)



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