Intermediate disorder limits for multi-layer semi-discrete directed polymers

Abstract

We show that the partition function of the multi-layer semi-discrete directed polymer converges in the intermediate disorder regime to the partition function for the multi-layer continuum polymer introduced by O'Connell and Warren. This verifies, modulo a previously hidden constant, an outstanding conjecture proposed by Corwin and Hammond. A consequence is the identification of the KPZ line ensemble as logarithms of ratios of consecutive layers of the continuum partition function. Other properties of the continuum partition function, such as continuity, strict positivity and contour integral formulas to compute mixed moments, are also identified from this convergence result.

50 pages, 2 figures

References in corpus (4)

• The crossing probability for directed polymers in random media
• Intermediate disorder directed polymers and the multi-layer extension of the stochastic heat equation
• Decorated Young Tableaux and the Poissonized Robinson-Schensted Process
• The stochastic heat equation, 2D Toda equations and dynamics for the multilayer process

Cited by in corpus (6)

• Shift-invariance for vertex models and polymers
• The KPZ equation in a half space with flat initial condition and the unbinding of a directed polymer from an attractive wall
• Central moments of the free energy of the O'Connell-Yor polymer
• Moments of the SHE under delta initial measure
• Jointly invariant measures for the Kardar-Parisi-Zhang Equation
• A stationary model of non-intersecting directed polymers