Speaker: Alexandre Stauffer (Roma Tre)
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.