Title: Multi-scale analysis of reaction-diffusion particle systems

6 Lectures:
Monday, 25 November at 16:30
Tuesday, 26 November at 14:30
Monday, 2 December at 16:30
Tuesday, 3 December at 14:30
Monday, 9 December at 16:30
Tuesday, 10 December at 14:30


All lectures will be in Room 211 (2nd floor) at
Department of Mathematics and Physics of Roma Tre
Largo San Murialdo 1, Palazzina C


For PhD students that want to take the course as part of their PhD 
coursework, the course will be completed by a reading part (to be 
discussed with the lecturer).


Abstract:
This course focus on the (microscopic) analysis of stochastic 
processes on particle systems. A few examples include spread of 
infection among moving particles, the frog model or stochastic 
combustion model, activated random walks, growth processes with 
competition, and branching random walk with interactions. A common 
feature of such models is that correlations do not decay exponentially 
fast, which brings serious challenges to the application of standard 
techniques of analysis, such as renormalization techniques and 
comparison with independent percolation.

Recently, there has been very important progress in this field, with 
most new results employing a so-called multi-scale analysis to control 
the dependences in the model. Multi-scale analysis proved to be an 
extremely powerful technique; it has been employed in areas beyond 
particle system, one notable example being the study of random 
interlacements, where it has been playing a fundamental role. Despite 
its power, a multi-scale analysis can be quite involved to implement 
and can become very technical. In particular, it usually needs to be 
developed from scratch for each application as it needs to be tailored 
to each specific question being analyzed.

The goal of this course is to explain the multi-scale analysis in a 
didactic and comprehensible way, demystifying this technique, and 
explaining its main aspects (the ones that are common to most
applications) and the most common variations.
In order to do this we will concentrate on one problem: the analysis 
of the spread of an infection among particles that move as independent 
simple random walks.