##### Department of Mathematics,

University of California San Diego

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### Math 288 - Probability & Statistics

## Qiang Zeng

#### Northwestern University

## The Sherrington-Kirkpatrick model is Full-step Replica Symmetry Breaking at zero temperature

##### Abstract:

Starting in 1979, the physicist Giorgio Parisi wrote a series of ground breaking papers introducing the idea of replica symmetry breaking, which allowed him to predict a solution for the Sherrington-Kirkpatrick (SK) model by breaking the symmetry of replicas infinitely many times. This is known as full-step replica symmetry breaking (FRSB). In this talk, we will provide a mathematical proof of Parisi's FRSB prediction at zero temperature for the more general mixed p-spin model. More precisely, we will show that the functional order parameter of this model is not a step function. This talk is based on joint work with Antonio Auffinger and Wei-Kuo Chen.

Host: Tianyi Zheng

### November 2, 2017

### 10:00 AM

### AP&M 6402

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