KPZ Scaling Theory and the Semi-discrete Directed Polymer Model

Abstract

We explain how the claims of the KPZ scaling theory are confirmed by a recent proof of Borodin and Corwin on the asymptotics of the semi-discrete directed polymer.

typo corrected in Eq. (2.24)

References in corpus (5)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• Growing interfaces uncover universal fluctuations behind scale invariance
• Asymptotics in ASEP with Step Initial Condition
• Exact scaling functions for one-dimensional stationary KPZ growth
• Fluctuation properties of the TASEP with periodic initial configuration

Cited by in corpus (19)

• A KPZ Cocktail- Shaken, not stirred: Toasting 30 years of kinetically roughened surfaces
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• A phase transition for $q$-TASEP with a few slower particles
• Macdonald processes, quantum integrable systems and the Kardar-Parisi-Zhang universality class
• Tracy-Widom asymptotics for q-TASEP
• Facilitated exclusion process
• Searching for the Tracy-Widom distribution in nonequilibrium processes
• Anomalous fluctuations for a perturbed Hamiltonian system with exponential interactions
• The $q$-Hahn asymmetric exclusion process
• Large Deviations For Sticky Brownian Motions
• Whittaker functions and related stochastic processes
• Tracy-Widom limit of q-Hahn TASEP
• KPZ universality class and the anchored Toom interface
• Stochastic growth in time dependent environments
• Uniqueness and ergodicity of stationary directed polymers on ${\mathbb{Z}}^2$
• Stationary Higher Spin Six Vertex Model and $q$-Whittaker measure
• Fluctuations of TASEP and LPP with general initial data
• Point-interacting Brownian motions in the KPZ universality class
• Asymptotic fluctuations of geometric q-TASEP, geometric q-PushTASEP and q-PushASEP