# Non-existence of bi-infinite polymer Gibbs measures on Z^2

Speaker
Ofer Busani, University of Bristol
Date
21/03/2021 - 13:00 - 12:00Add to Calendar 2021-03-21 12:00:00 2021-03-21 13:00:00 Non-existence of bi-infinite polymer Gibbs measures on Z^2 To each vertex x\in  Z^2 assign a positive weight \omega_x. A geodesic between two ordered points on the lattice is an up-right path maximizing the cumulative weight along itself.  A bi-infinite geodesic is an infinite path taking up-right steps on the lattice and such that for every two points on the path, its restriction to between the points is a geodesic. Assume the weights across the lattice are  i.i.d.,  does there exist a bi-infinite geodesic with some positive probability? In the case the weights are Exponentially distributed, we answer this question in the negative. We show an analogous result for the positive-temperature variant of this model. Joint work with Marton Balazs and Timo Seppalainen.             ZOOM: https://us02web.zoom.us/j/89074854473?pwd=R1BWVEZ4NG5yMkhNYVB2RGRLVnNMdz09 אוניברסיטת בר-אילן - המחלקה למתמטיקה mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
ZOOM: https://us02web.zoom.us/j/89074854473?pwd=R1BWVEZ4NG5yMkhNYVB2RGRLVnNMdz09
Abstract

To each vertex x\in  Z^2 assign a positive weight \omega_x. A geodesic between two ordered points on the lattice is an up-right path maximizing the cumulative weight along itself.  A bi-infinite geodesic is an infinite path taking up-right steps on the lattice and such that for every two points on the path, its restriction to between the points is a geodesic. Assume the weights across the lattice are  i.i.d.,  does there exist a bi-infinite geodesic with some positive probability?

In the case the weights are Exponentially distributed, we answer this question in the negative. We show an analogous result for the positive-temperature variant of this model.

Joint work with Marton Balazs and Timo Seppalainen.

תאריך עדכון אחרון : 15/03/2021