Il Prof. Yuri Kondratiev [Fakultät für Mathematik Universität Bielefeld ] sarà ospite del Dipartimento di Informatica dell’Università di Verona [ Strada le Grazie, 15 - Vr ] nei giorni dal 27 al 31 Ottobre 2014 e terrà il seguente mini corso [8 ore]
Statistical dynamics for interaction particle systems
articolato in tre lezioni, che si terranno nell'edificio Ca' Vignal 2 - Aula M, nei giorni
- Lunedì 27 Ottobre [ 13:30-16:30 ] - Mercoledì 29 Ottobre [ 15:30-18:30 ] - Giovedì 30 Ottobre [ 13:30-15:30 ]
con il seguente programma
*Abstract*
We 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*
1. Configuration spaces 2.
Harmonic analysis on configuration spaces 3.
Statistical Markov evolutions and hierarchical chains 4.
Birth-and-death Markov processes on configuration spaces 5.
Conservative stochastic dynamics 6.
Mesoscopic scalings and kinetic equations 7.
Multicomponent systems 8.
Applications
(a) Mathematical physics
(b) Ecological models
(c) Cancer modeling
(d) Social models
Per informazioni contattare: luca.dipersio@univr.it
__ Luca Di Persio - PhD assistant professor of Probability and Mathematical Finance
Dept. Informatics University of Verona strada le Grazie 15 - 37134 Verona - Italy Tel : +39 045 802 7968
Dept. Math University of Trento V. Sommarive, 14 - 38123 Povo - Italy Tel : +39 0461 281686