An identity in distribution between fullspace and halfspace loggamma polymers
Abstract
We prove an identity in distribution between two kinds of partition functions for the loggamma directed polymer model: (1) the pointtopoint partition function in a quadrant, (2) the pointtoline partition function in an octant. As an application, we prove that the pointtoline free energy of the loggamma polymer in an octant obeys a phase transition depending on the strength of the noise along the boundary. This transition of (de)pinning by randomness was first predicted in physics by Kardar in 1985 and proved rigorously for zero temperature models by Baik and Rains in 2001. While it is expected to arise universally for models in the KardarParisiZhang universality class, this is the first positive temperature model for which this transition can be rigorously established.
 Publication:

arXiv eprints
 Pub Date:
 August 2021
 arXiv:
 arXiv:2108.08737
 Bibcode:
 2021arXiv210808737B
 Keywords:

 Mathematics  Probability;
 Mathematical Physics;
 Mathematics  Combinatorics
 EPrint:
 34 pages, 8 Figures. v2: minor edits