2024 Fall MATH C223A 001 LEC 001

2024 Fall

MATH C223A 001 - LEC 001

Advanced Topics in Probability and Stochastic Process

Geometric aspects of high dimensional Gibbs measures

Shirshendu Ganguly

Aug 28, 2024 - Dec 13, 2024
Tu, Th
12:30 pm - 01:59 pm
Class #:33574
Units:3

Instruction Mode: In-Person Instruction

Offered through Mathematics

Current Enrollment

Total Open Seats: 1
Enrolled: 4
Waitlisted: 0
Capacity: 5
Waitlist Max: 5
No Reserved Seats

Hours & Workload

6 hours of outside work hours, and 3 hours of instructor presentation of course materials.

Other classes by Shirshendu Ganguly

Course Catalog Description

The topics of this course change each semester, and multiple sections may be offered. Advanced topics in probability offered according to students demand and faculty availability.

Class Description

Description: High dimensional Gibbs measures are ubiquitous in probability theory, statistical mechanics and theoretical computer science. A generic example, say on the hypercube Q=\{-1,1\}^n, is given by a Hamitonian H: Q o \mathbb{R}, with the measure \mu at \sigma \in Q being proportional to \exp\left(-eta H(\sigma) ight) where eta>0 is the inverse temperature parameter. Z, the normalizing constant, is known as the partition function. Central examples include the Ising model, spin glass models, exponential random graphs, the hardcore model and so on. Such Gibbs measures also admit natural Glauber dynamics which keep \mu stationary. The energy landscape induced by the Hamiltonian can often be quite complicated admitting exponentially many near ground states (the ground state is the state with the minimal energy). In this course we will learn various techniques to estimate the partition function as well as establish structure theorems for a variety of Gibbs measures and the behavior of the associated Glauber dynamics. Phenomena such as super-concentration, chaos, multiple valleys and peaks, replica symmetry/breaking and metastability will be explored. We will assume familiarity with the basics of graduate probability equivalent to Stat C205A.

Rules & Requirements

Repeat Rules

Reserved Seats

Current Enrollment

No Reserved Seats

Textbooks & Materials

See class syllabus or https://calstudentstore.berkeley.edu/textbooks for the most current information.

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