Exact Scaling Functions for One-Dimensional Stationary KPZ Growth
By Michael Praehofer, Herbert Spohn. 2002
257 citations recorded by the source corpus.
We determine the stationary two-point correlation function of the one-dimensional KPZ equation through the scaling limit of a solvable microscopic model, the polynuclear growth model. The equivalence to a directed polymer problem with specific boundary conditions allows one to express the corresponding scaling function in terms of the solution to a Riemann–Hilbert problem related to the Painlevé II equation. We solve these equations numerically with very high precision and compare our, up to numerical rounding exact, result with the prediction of Colaiori and Moore(1) obtained from the mode coupling approximation.
Subfields: Condensed Matter Physics, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/441972364a2ac034c1d4be30b43335fae3c2f196
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In Condensed Matter Physics
In Mathematical Physics
In Statistics and Probability
Citations in the corpus
- An appetizer to modern developments on the Kardar–Parisi–Zhang universality class (2017, background): “For the stationary subclass, too, the two-point function defined analogously decays superexponentially, g0(ζ) ∼ e−c0 |ζ | 3 with a coefficient c0 different from c1 [99, 103].”
- The nonperturbative functional renormalization group and its applications (2020, methodology): “Figure 8: Comparison of the scaling functions f (y) (left panel) and f̃ (k) (right panel) obtained from FRG (red curves with dots) [422, 425] with the exact ones (black curves with squares) [426].”
- Scaling Limit for the Space-Time Covariance of the Stationary Totally Asymmetric Simple Exclusion Process (2005, methodology): “For the TASEP we have to develop a novel method which will be rather different from [2, 21] and uses non-intersecting line ensembles.”
- Nonlinear Fluctuating Hydrodynamics for Anharmonic Chains (2013, methodology): “As a supporting approach, discrete models have been studied, like the PNG model [51,14] and the TASEP [52].”
- Nonperturbative effects and nonperturbative definitions in matrix models and topological strings (2008, methodology): “We conclude that the Hastings–McLeod solution, which is the nonpertubative solution to the doubly-scaled unitary matrix model (and to many other models, see for example [76, 69]) has the trans-series expansion”
- The Surprising Mathematics of Longest Increasing Subsequences (2015, methodology): “1 was generated from numerical data computed by Prähofer and Spohn [102].”
- Height Fluctuations for the Stationary KPZ Equation (2014, methodology): “Indeed, we recover the distribution formula obtained before for the totally asymmetric simple exclusion process and for the polynuclear growth model [3, 4, 11, 14].”