Non-equilibrium Dynamics and Random Matrices | |

Topic: | Self-avoiding walk in dimension 4 |

Speaker: | Roland Bauerschmidt |

Affiliation: | Member, School of Mathematics |

Date: | Tuesday, January 28 |

Time/Room: | 2:00pm - 3:00pm/S-101 |

Video Link: | https://video.ias.edu/nedrm/2014/0128-RolandBauerschmidt |

The (weakly) self-avoiding walk is a basic model of paths on the d-dimensional integer lattice that do not intersect (have few intersections), of interest from several different perspectives. I will discuss a proof that, in dimension 4, the susceptibility of the weakly self-avoiding walk diverges with an explicit logarithmic correction as the critical point is approached. The argument is based on a representation of the weakly self-avoiding walk as a supersymmetric field theory which is studied with a renormalization group method. This is joint work with Brydges and Slade.