A multi-layer extension of the stochastic heat equation

Abstract

Motivated by recent developments on solvable directed polymer models, we define a 'multi-layer' extension of the stochastic heat equation involving non-intersecting Brownian motions.

v4: substantially extended and revised version

References in corpus (11)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• Asymptotics in ASEP with Step Initial Condition
• The intermediate disorder regime for directed polymers in dimension $1+1$
• Kesten's theorem for Invariant Random Subgroups
• A Fredholm Determinant Representation in ASEP
• The Continuum Directed Random Polymer
• Tropical Combinatorics and Whittaker functions
• Geometric RSK correspondence, Whittaker functions and symmetrized random polymers
• The One-dimensional KPZ Equation and the Airy Process
• Two-point generating function of the free energy for a directed polymer in a random medium
• Formulas for Joint Probabilities for the Asymmetric Simple Exclusion Process

Cited by in corpus (16)

• Quantum causal modelling
• The directed landscape
• Macdonald processes, quantum integrable systems and the Kardar-Parisi-Zhang universality class
• Transversal fluctuations of the ASEP, stochastic six vertex model, and Hall-Littlewood Gibbsian line ensembles
• Intermediate disorder limits for multi-layer semi-discrete directed polymers
• Tilted elastic lines with columnar and point disorder, non-Hermitian quantum mechanics and spiked random matrices: pinning and localization
• Height fluctuations for the stationary KPZ equation
• Whittaker functions and related stochastic processes
• Intermediate disorder directed polymers and the multi-layer extension of the stochastic heat equation
• Brownian bridges for late time asymptotics of KPZ fluctuations in finite volume
• Charged String Tensor Networks
• Mutually avoiding paths in random media and largests eigenvalues of random matrices
• The stochastic heat equation, 2D Toda equations and dynamics for the multilayer process
• Brownian regularity for the KPZ line ensemble
• A stationary model of non-intersecting directed polymers
• Local solution to the multi-layer KPZ equation