21pYO-3 Spatial correlations of the 1D KPZ surface on a flat substrate

By Tomohiro Sasamoto. 2005

213 citations recorded by the source corpus.

We study the spatial correlations of the one-dimensional KPZ surface for the flat initial condition. It is shown that the multi-point joint distribution for the height is given by a Fredholm determinant, with its kernel in the scaling limit explicitly obtained. This may also describe the dynamics of the largest eigenvalue in the GOE Dyson's Brownian motion model. Our analysis is based on a reformulation of the determinantal Green's function for the totally ASEP in terms of a vicious walk problem.

Subfields: Condensed Matter Physics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a186d3e2057fb5a701822aa7c8236f58974c45dc

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Citations in the corpus

Scaling Limit for the Space-Time Covariance of the Stationary Totally Asymmetric Simple Exclusion Process (2005, background): “As established by Sasamoto [22], see also [7], the single point statistics in the limit of large times is then given by the distribution of the largest eigenvalue of the GOE of random matrices and thus different from the distribution obtained in this contribution.”
Fluctuation Properties of the TASEP with Periodic Initial Configuration (2006, background): “Since in this paper we explain the detail of the derivation in [34], it is useful to point out a difference.”
Evidence for Geometry-Dependent Universal Fluctuations of the Kardar-Parisi-Zhang Interfaces in Liquid-Crystal Turbulence (2012, result): “Moreover, given the expected equivalence of the asymptotic spatial profile of the flat and circular interfaces to the Airy1 and Airy2 processes [10, 12, 73, 75, 80], respectively, our results may also shed light on the temporal persistence of the Airy processes, as well as, for the circular case, th”
The One-Dimensional KPZ Equation and Its Universality Class (2015, background): “with kernel Bs(x, y) = Ai(x+ y + s), see [32, 33] for this particular representation.”
Introduction to KPZ (2011, background): “) Airy1 arises in growth models starting from flat initial data and point-to-line random polymers [105],[23].”
An appetizer to modern developments on the Kardar–Parisi–Zhang universality class (2017, background): “Analytic expressions for such limiting processes have been obtained for the the circular and flat subclasses [70], and named the Airy2 processA2(ζ) for the circular case [66, 97] and the Airy1 processA1(ζ) for the flat case [83, 98].”
A pedestrian's view on interacting particle systems, KPZ universality and random matrices (2008, background): “Subsequently Sasamoto identified the analogous process for the case of flat initial conditions (case I) [109].”
Height Fluctuations for the Stationary KPZ Equation (2014, unknown): “These statistical properties agreed between the models, but depended non-trivially on the type of initial data or geometry for the growth models, such as curved [6, 10, 21, 22, 60, 61, 68], flat [10, 21, 23–25, 43, 48, 73] or stationary [7–9, 47, 49, 57, 69].”