11:00-12:15, Every Thursday from October 18 to November 29, 2018
Math Mini-Course by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
Although Markov processes such as random walks or Brownian motion have been ubiquitous in all kinds of stochastic models for many decades, their importance in the study of other processes notably the models of statistical physics became recently more obvious.
We describe the emergence of a mathematical scenery in which Markovian constructions play a fundamental role, where a variety of processes are fundamentally connected: Loop ensembles, random spanning trees, configuration models, networks, flows and maps are part of this picture and relations with the physical field theory are in the background.
The course will present several aspects of the theory. Here is a (tentative) list:
1. Weighted graphs, Markov chains and loop measures.
2. Loop erasure and spanning trees.
3. The Gaussian free field. Bosons and Fermions.
4. Networks, configurations and maps.
5. Loop topology and Gauge fields.
6. Brownian loops and renormalization.