Collective behavior of large stochastic systems

Kotecký, Roman ; Biskup, Marek
Czech Science Foundation 16-15238S board no. P201

Large stochastic systems of interacting components often exhibit collective behavior, where despite, or even thanks to noise on the individual level, the components of the system conspire to form ordered structures, sometimes of an unexpected nature, on large scales. This may be observed when molecules organize themselves into a liquid or crystal, or form a sharp interface between two phases, but also in the distribution of limit orders on a stock market or emails of different priorities in a mailbox waiting to be answered, and in seemingly abstract mathematical problems about random colourings of graphs or the emergence of large cycles in random permutations.
We propose 19 explicit problems of varied level of difficulty organized in 8 interconnected work-packages, to be studied using a large array of rigorous mathematical methods.

Principal investigator: Roman Kotecký
Researcher: Marek Biskup