2015/03/03 by Partha S. Dey, Dey, Partha S., Nikos Zygouras +1
Mathematics · #60G70 #82D60 #Combinatorics #Conjecture #Exponent #Exponential function #FOS: Mathematics #Gamma distribution #Inverse #Inverse temperature #Limit (mathematics) #Limiting #Markov Chains and Monte Carlo Methods #Mathematical analysis #Mathematical physics #Mathematics #Partition (number theory) #Partition function (quantum field theory) #Physics #Primary: 60F05 #Probability (math.PR) #Quantum mechanics #Random Matrices and Applications #Scaling #Secondary: 60G57 #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Thermodynamics #Universality (dynamical systems) #math.PR #msc:60F05 #msc:60G57 #msc:60G70 #msc:82D60
paper · pdf · doi:10.48550/arxiv.1503.01054
published in arXiv (Cornell University) (Cornell University) · 33 pages, 1 figure
arxiv created 2015/03/03 · openalex publication_date 2015/03/03 · arxiv updated 2015/03/04 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
The directed polymer model at intermediate disorder regime was introduced by\nAlberts-Khanin-Quastel~ citeAKQ12. It was proved that at inverse temperature\n\β n-\γ with \γ=1/4 the partition function, centered\nappropriately, converges in distribution and the limit is given in terms of the\nsolution of the stochastic heat equation. This result was obtained under the\nassumption that the disorder variables posses exponential moments, but its\nuniversality was also conjectured under the assumption of six moments. We show\nthat this conjecture is valid and we further extend it by exhibiting classes of\ndifferent universal limiting behaviors in the case of less than six moments. We\nalso explain the behavior of the scaling exponent for the log-partition\nfunction under different moment assumptions and values of \γ.\n