Multitime Distribution in Discrete Polynuclear Growth
Kurt Johansson, Mustazee Rahman
Abstract
Abstract We study the multitime distribution in a discrete polynuclear growth model or, equivalently, in directed last‐passage percolation with geometric weights. A formula for the joint multitime distribution function is derived in the discrete setting. It takes the form of a multiple contour integral of a block Fredholm determinant. The asymptotic multitime distribution is then computed by taking the appropriate KPZ‐scaling limit of this formula. This distribution is expected to be universal for models in the Kardar‐Parisi‐Zhang universality class. © 2021 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.
Topics & Concepts
Fredholm determinantMathematicsUniversality (dynamical systems)Discrete time and continuous timeDistribution (mathematics)ScalingStatistical physicsPercolation (cognitive psychology)ZhàngLimit (mathematics)Mathematical analysisApplied mathematicsPhysicsGeometryStatisticsQuantum mechanicsBiologyLawPolitical scienceNeuroscienceChinaRandom Matrices and ApplicationsStochastic processes and statistical mechanicsTheoretical and Computational Physics