# Spring 2016 MATH C223B 001 LEC

Section | Days/Time | Location | Instructor | CCN |
---|---|---|---|---|

001 LEC | TuTh 1230-2P | 334 EVANS | HAMMOND, A | 54491 |

Units/Credit | Final Exam Group | Enrollment |
---|---|---|

3 | NONE | Limit:10 Enrolled:2 Waitlist:0 Avail Seats:8 [on 02/29/16] |

**Note:** "Self-avoiding walk" - Self-avoiding walk of length n on the integer lattice Z^d is the uniform measure on the set of nearest neighbor paths of length n from the origin that never revisit a vertex. Studying large scale properties of the measure, such as the typical distance from the origin of its other endpoint, is a famously difficult problem. The class will discuss several classical and recent aspects of rigorous research. Cross-listed with Statistics C206B

**Prerequisites:**

**Description:** Self-avoiding walk.

Self-avoiding walk of length \(n\) on the integer lattice \(Z^d\) is the uniform measure on the set of nearest neighbour paths of length \(n\) from the origin that never revisit a vertex. Studying large scale properties of the measure, such as the typical distance from the origin of its other endpoint, is a famously difficult problem. The class will discuss several classical and recent aspects of rigorous research. Beginning with classical results concerning local geometry (Kesten's pattern theorem) and corrections to exponential growth for walk number (the Hammersley-Welsh bound), we will also discuss recent work, including techniques from discrete complex analysis that in an argument of Duminil-Copin and Smirnov determine the value of exponential growth for walk number for hexagonal lattice; sub-ballisticity of the walk, and several techniques for gauging the "closing probability", that the walk ends adjacent to the origin.

**Office:** 791 Evans

**Office Hours:**

**Required Text:**

**Recommended Reading:**

**Grading:** Letter grade.

**Homework:**

**Course Webpage:**