**Topic:** Markovian Probability**Date & Time:** Thursday, October 18, 2018 - 11:00 to Thursday, November 29, 2018 - 12:15**Speaker:** Yves Le Jan, Université Paris-Sud & NYU Shanghai**Location:** Room 304, NYU Shanghai, 1555 Century Avenue (世纪大道 1555号上海纽约大学浦东教学楼 304 室)

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The Mini-Course is sponsored by NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai.

© 2018 NYU Shanghai

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**Thursdays, October 18 - November 29 , 2018**

**Abstract:**

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.

**Biography:**

Yves Le Jan is Visiting Professor of Mathematics at NYU Shanghai. He has been working mostly on various aspect of stochastic processes. He is particularly interested in their relations to Mathematical Physics. He was for eight years an associate editor of the Annals of Probability, edited by the IMS. He was invited to give a lecture at the International Congress of Mathematicians in 2006 and to give the plenary Doob lecture at the World Congress of Probability and Statistics in 2012.