Statistical dynamics for interaction particle systemsarticolato in tre lezioni, che si terranno nell'edificio Ca' Vignal 2 - Aula M, nei giorni
con il seguente programma
- Lunedì 27 Ottobre [ 13:30-16:30 ]
- Mercoledì 29 Ottobre [ 15:30-18:30 ]
- Giovedì 30 Ottobre [ 13:30-15:30 ]
AbstractWe will discuss an approach to modeling of real world phenomena by interacting particle systems in the continuum. In many cases, evolutions of considered systems may be described as Markov stochastic processes. Related statistical dynamics are evolutions of macroscopic states associated with the forward Kolmogorov (or Fokker-Planck) equations for these Markov processes. We will study statistical dynamics in terms of corresponding hierarchical chains of evolution equations for correlation functions. These chains admit mesoscopic scalings that leads to kinetic evolution equations for densities of considered systems. Particular examples which will be discussed include models from mathematical physics, ecology, cell biology and socio-economic models. Between other aspects these examples illustrate such notions as dynamical phase transitions, non-local evolution equations, front propagation, self-aggregation, effects of environment fluctuations etc.
Tentative program
Harmonic analysis on configuration spaces
Statistical Markov evolutions and hierarchical chains
Birth-and-death Markov processes on configuration spaces
Conservative stochastic dynamics
Mesoscopic scalings and kinetic equations
Multicomponent systems
Applications
(a) Mathematical physics
(b) Ecological models
(c) Cancer modeling
(d) Social models