The 2023 Fall School in Probability II is part of the PKU Thematic Semester Program on Stochastics to celebrate the 110th anniversary of Mathematical Sciences at Peking University. 

Dates: 

23--27 October, 2023

Venue:

Jia Yi Bing Lecture Hall, Beijing International Center for Mathematical Research

Lecturers and titles:

·Christophe Garban (Lyon): Phase transitions in continuous spin systems

·Vadim Gorin (UC Berkeley): Six vertex model and random matrix distributions

Abstracts:

Garban:

The goal of this mini-course will be to give an introduction to spin systems defined on a lattice Z^d with an underlying continuous symmetry. This includes the following examples:
- The Gaussian Free Field whose 'spins' are R valued
- The Villain and XY models whose spins are S^1 valued
- The classical Heisenberg model with values in S^2
- Lattice gauge theory with continuous gauge group G

Some of the classical techniques which are very powerful when dealing with a discrete symmetry spin system (for example the so-called Peierls argument for the Ising model) do not apply for continuous symmetry spin systems. This mini-course will explain how such continuous symmetries affect the fluctuations in the system and will introduce some of the main relevant techniques, among which:
- Mermin-Wagner theorem (on the absence of long-range order in 2d)
- Reflection positivity
- techniques from Bayesian statistics 

(if time permits, I will also talk about duality transformations and topological defects). 

Gorin:

In these lectures we will introduce the six-vertex (square ice) model, discuss the key tools in its study, and connect it to the random matrix theory. I plan to cover most of the notes arXiv:2309.12495. 

Registration

Participants are expected to arrange their own meals and accommodation. 

Participants who need us help arrange access to the PKU campus should register by 4pm Sunday 8 October. 

PhD students and postdocs should also ask their advisor to send a reference letter to probability@math.pku.edu.cn by the same date.

Please scan the QR code or click the URL to complete the registration.

https://www.wjx.cn/vm/evhfLEI.aspx