Characterizing stationary 1+1 dimensional lattice polymer models

2017/08/23 by Hans Chaumont, Chaumont, Hans, Christian Noack +1 · 1 citation
Mathematics · Physics and Astronomy · #60K35 #60K37 #82B23 #82D60 #FOS: Mathematics #FOS: Physical sciences #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #math.PR #msc:60K35 #msc:60K37 #msc:82B23 #msc:82D60

paper · pdf · doi:10.48550/arxiv.1708.07187

21 pages, 5 figures

arxiv created 2017/08/23 · arxiv updated 2017/08/25

Abstract

Motivated by the study of directed polymer models with random weights on the square integer lattice, we define an integrability property shared by the log-gamma, strict-weak, beta, and inverse-beta models. This integrability property encapsulates a preservation in distribution of ratios of partition functions which in turn implies the so called Burke property. We show that under some regularity assumptions, up to trivial modifications, there exist no other models possessing this property.

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• Ultra-Discretization of Yang-Baxter Maps, Probability Distributions and Independence Preserving Property

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