The Critical Disordered Pinning Measure
Time: 2023-11-09
Published By: He Liu
Speaker(s): Ran Wei(Xi'an Jiaotong-Liverpool University)
Time: 10:00-11:30 November 16, 2023
Venue: Room 78201, Jingchunyuan 78, BICMR
The \textit{disordered pinning model} is a statistical mechanical model that depicts the interaction between a polymer chain and a membrane. The polymer chain is represented by a renewal process and the membrane is represented by a sequence of random variables (also called the \textit{disorder}) indexed by time. At each renewal time, the distribution of the renewal process is exponentially tilted by the disorder. In this talk, we first review some properties and known results for this model, and then we introduce our result. We show that when the disorder is marginally relevant and the temperature is in a critical window, then the partition functions of the model converge weakly to a random measure on time. This is a joint work with Jinjiong Yu.
