## View abstract

### Session S38 - Geometric Potential Analysis

Monday, July 19, 19:00 ~ 19:30 UTC-3

## On the dynamical network of interacting particles: from micro to macro

### Ewelina Zatorska

#### Imperial College London, UK   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak320b2037dbc93b832099e25f09efeab2').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy320b2037dbc93b832099e25f09efeab2 = '&#101;.z&#97;t&#111;rsk&#97;' + '&#64;'; addy320b2037dbc93b832099e25f09efeab2 = addy320b2037dbc93b832099e25f09efeab2 + '&#105;mp&#101;r&#105;&#97;l' + '&#46;' + '&#97;c' + '&#46;' + '&#117;k'; var addy_text320b2037dbc93b832099e25f09efeab2 = '&#101;.z&#97;t&#111;rsk&#97;' + '&#64;' + '&#105;mp&#101;r&#105;&#97;l' + '&#46;' + '&#97;c' + '&#46;' + '&#117;k';document.getElementById('cloak320b2037dbc93b832099e25f09efeab2').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy320b2037dbc93b832099e25f09efeab2 + '\'>'+addy_text320b2037dbc93b832099e25f09efeab2+'<\/a>';

In this talk I will present a derivation of macroscopic model of interacting particles. The population of N particles evolve according to a diffusion process and interacts through a dynamical network. In turn, the evolution of the network is coupled to the particles' positions. In contrast with the mean-field regime, in which each particle interacts with every other particle, i.e. with O(N) particles, we consider the a priori more difficult case of a sparse network; that is, each particle interacts, on average, with O(1) particles. We also assume that the network's dynamics is much faster than the particles' dynamics. The derivation combines the stochastic averaging (over time-scale parameter) and the many particles ($N\to \infty$) limits.