2017/11/22 by Hans Chaumont, Chaumont, Hans, Christian Noack +1 · 1 citation
Mathematics · Physics and Astronomy · #60K35 #60K37 #82B20 #82B23 #82D60 #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #math.PR #msc:60K35 #msc:60K37 #msc:82B20 #msc:82B23 #msc:82D60
paper · pdf · doi:10.48550/arxiv.1711.08432
33 pages, 8 figures
arxiv created 2017/11/22 · openalex publication_date 2017/11/22 · arxiv updated 2017/11/23 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
We develop a Mellin transform framework which allows us to simultaneously analyze the four known exactly solvable 1+1 dimensional lattice polymer models: the log-gamma, strict-weak, beta, and inverse-beta models. Using this framework we prove the conjectured fluctuation exponents of the free energy and the polymer path for the stationary point-to-point versions of these four models. The fluctuation exponent for the polymer path was previously unproved for the strict-weak, beta, and inverse-beta models.