# Charles River Lectures 2014

# The 2014 Charles River Lectures on Probability and Related Topics

**October 17, 2014**

Jointly organized by Harvard University, Massachusetts Institute of Technology, and Microsoft Research New England, the Charles River Lectures on Probability and Related Topics is a one-day event for the benefit of the greater Boston area mathematics community. The 2014 lectures will take place 9:30am – 5:30pm on Friday, October 17 at Harvard University in the **Tsai Auditorium** (Room S010) in the **CGIS South building (1730 Cambridge Street, Cambridge, MA 02138)**.

# PLEASE NOTE: **LOCATION CHANGE**

## The Lectures will now be held in:

**Tsai Auditorium** (Room S010) in the **CGIS South building (1730 Cambridge Street, Cambridge, MA 02138)**.

**Registration**

**Please note that registration has closed.**

For questions regarding the event, please email charlesriverlectures2014@gmail.com

**Date and Location**

- Where:
**Tsai Auditorium**(Room S010) in the**CGIS South building (1730 Cambridge Street, Cambridge, MA 02138)**. - When: 9:30 AM – 5:30 PM —— October 17, 2014
- Cost: FREE

**Speakers**

- David Brydges
*(University of British Columbia)* - Sourav Chatterjee
*(Stanford University)* - Christophe Garban
*(Université Lyon 1**)* - Fabio Toninelli
*(CNRS & Institut Camille Jordan, Lyon 1)* - Srinivasa Varadhan
*(New York University)*

**Agenda**

The event features five lectures by distinguished researchers in the areas of probability and related topics.

- 9:30 AM – 9:50 AM: Registration and Coffee

- 9:50 AM – 10:00 AM: Opening Remarks

- 10:00 AM – 11:00 AM: Srinivasa Varadhan
*(New York University)*

The role of compactness in large deviations.The estimates obtained in large deviations are basically local estimates. While it is not a problem for lower bounds it is a problem for upper bounds. In the absence of exponential tightness some type of “compactification” of the space is needed. We will look at a few examples.

- 11:10 AM. – 12:10 PM: Sourav Chatterjee
*(Stanford University)*

Nonlinear large deviationsClassical large deviations theory is mainly a linear theory. This is demonstrated by the fact that there are no ready-to-use classical tools that can handle large deviations for even the simplest nonlinear functionals, such as triangles in random graphs. In this talk I will present a new theory whose long-term goal is to extend large deviations to the nonlinear setting. The current version of this theory can handle basic nonlinear functionals of Bernoulli random variables. As a specific application, I will discuss how this theory solves the question of large deviations for subgraph counts in certain sparse random graphs. Previous theory, based on Szemeredi’s regularity lemma, could only handle dense graphs. This is joint work with Amir Dembo.

- 12:10 PM – 1:40 PM: Lunch Break

- 1:40 PM – 2:40 PM: David Brydges
*(University of British Columbia)*

Analysis of critical lattice spin models by renormalisation group

- 2:50 PM – 3:50 PM: Christophe Garban
*(Université Lyon 1**)*

Near-critical percolation and minimal spanning tree in the planeSample N points uniformly in a unit square of the plane. Among all the spanning trees which cover these N points, consider the tree with minimal euclidean length, called the Minimal Spanning Tree. In this talk, I will explain how to construct a continuous tree embedded in the plane which should be the scaling limit as N goes to infinity of the above tree. With such a Poissonian way of defining a planar minimal spanning tree, this limiting behaviour still remains conjectural but if one considers instead the analogous model on a well chosen planar graph, much more can be done: in a joint work started long ago with Gabor Pete and Oded Schramm and completed only recently, we prove that this continuous tree of a new kind is the scaling limit of the minimal spanning tree defined on the triangular lattice. Standard universality arguments suggest that the limiting tree should not depend on the microscopic structure of the model.

- 3:50 PM – 4:20 PM: Afternoon Break

- 4:20 PM – 5:20 PM: Fabio Toninelli
*(CNRS & Institut Camille Jordan, Lyon 1)*

Dimer models, Glauber dynamics and height fluctuationsDimer models (random perfect matchings of an infinite bipartite graph) are an exactly solvable 2-d statistical mechanics model, that can be viewed as a random discrete interface. I will present recent developments in two very different directions: 1) the role of the “macroscopic shape” and of interface height fluctuations in the study of the relaxation to equilibrium of Glauber stochastic dynamics for dimer models 2) “universality” of the logarithmic growth of height fluctuations for non-exactly solvable, interacting dimer models at equilibrium.

Based on joint works with P. Caputo, B. Laslier, A. Giuliani, F. Martinelli, V. Mastropietro

**Organizers**:

**Alexei Borodin, Ivan Corwin, Alice Guionnet, Vadim Gorin, Scott Sheffield, and H.T. Yau**

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Previous Charles River Lectures: