New bounds for the free energy of directed polymers in dimension 1+1 and 1+2

Abstract

We study the free energy of the directed polymer in random environment in dimension 1+1 and 1+2. For dimension 1, we improve the statement of Comets and Vargas concerning very strong disorder by giving sharp estimates on the free energy at high temperature. In dimension 2, we prove that very strong disorder holds at all temperatures, thus solving a long standing conjecture in the field.

31 pages, 4 figures, final version, accepted for publication in Communications in Mathematical Physics

References in corpus (5)

• Fractional moment bounds and disorder relevance for pinning models
• Marginal relevance of disorder for pinning models
• A replica-coupling approach to disordered pinning models
• Exponential inequalities for martingales and asymptotic properties of the free energy of directed polymers in random environment
• Hierarchical pinning models, quadratic maps and quenched disorder

Cited by in corpus (26)

• Scaling for a one-dimensional directed polymer with boundary conditions
• The intermediate disorder regime for directed polymers in dimension $1+1$
• The 1+1-dimensional Kardar-Parisi-Zhang equation and its universality class
• Ratios of partition functions for the log-gamma polymer
• Pinning on a defect line: characterization of marginal disorder relevance and sharp asymptotics for the critical point shift
• Differing averaged and quenched large deviations for random walks in random environments in dimensions two and three
• Large deviation rate functions for the partition function in a log-gamma distributed random potential
• Variational formulas and disorder regimes of random walks in random potentials
• Two-point generating function of the free energy for a directed polymer in a random medium
• Localization Transition for Polymers in Poissonian Medium
• Influence of spatial correlation for directed polymers
• Busemann functions and Gibbs measures in directed polymer models on ${\mathbb{Z}}^2$
• Localization of directed polymers with general reference walk
• Large deviations and wandering exponent for random walk in a dynamic beta environment
• Directed polymers in a random environment with a defect line
• The scaling limit of the directed polymer with power-law tail disorder
• On the Long-range Directed Polymer Model
• Sharp asymptotics for the free energy of 1+1 dimensional directed polymers in an infinitely divisible environment
• High temperature behaviors of the directed polymer on a cylinder
• Directed polymers on infinite graphs
• A remark on the bound for the free energy of directed polymers in random environment in 1+2 dimension
• An Almost-Sure CLT for Stretched Polymers
• Short- and long-time path tightness of the continuum directed random polymer
• Absence of weak disorder for directed polymers on supercritical percolation clusters
• On the scaling properties of (2+1) directed polymers in the high temperature limit
• Free Energy of the Cauchy Directed Polymer Model at High Temperature