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Non-existence of bi-infinite polymer Gibbs measures | | Ofer Busani
; Timo Seppäläinen
; | | Date: |
21 Oct 2020 | | Abstract: | We show that nontrivial bi-infinite polymer Gibbs measures do not exist in
typical environments in the inverse-gamma (or log-gamma) directed polymer model
on the planar square lattice. The precise technical result is that, except for
measures supported on straight-line paths, such Gibbs measures do not exist in
almost every environment when the weights are independent and identically
distributed inverse-gamma random variables. The proof proceeds by showing that
when two endpoints of a point-to-point polymer distribution are taken to
infinity in opposite directions but not parallel to lattice directions, the
midpoint of the polymer path escapes. The proof is based on couplings, planar
comparison arguments, and a recently discovered joint distribution of Busemann
functions. | | Source: | arXiv, 2010.11279 | | Services: | Forum | Review | PDF | Favorites | |
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