Crossover between various initial conditions in KPZ growth: flat to stationary
نویسندگان
چکیده
منابع مشابه
Exact scaling functions for one-dimensional stationary KPZ growth
We determine the stationary two-point correlation function of the onedimensional 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...
متن کاملSlow decorrelations in KPZ growth
For stochastic growth models in the Kardar-Parisi-Zhang (KPZ) class in 1 + 1 dimensions, fluctuations grow as t1/3 during time t and the correlation length at a fixed time scales as t2/3. In this note we discuss the scale of time correlations. It turns out that the spacetime is non-trivially fibred, having slow directions with decorrelation exponent equal to 1 instead of the usual 2/3. These di...
متن کاملShort-time growth of a Kardar-Parisi-Zhang interface with flat initial conditions.
The short-time behavior of the (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) growth equation with a flat initial condition is obtained from the exact expressions for the moments of the partition function of a directed polymer with one end point free and the other fixed. From these expressions, the short-time expansions of the lowest cumulants of the KPZ height field are exactly derived. The resul...
متن کاملOptimal model selection for stationary data under various mixing conditions
The history of statistical model selection goes back at least to Akaike [Aka70], [Aka73] and Mallows [Mal73]. They proposed to select among a collection of parametric models the one which minimizes an empirical loss plus some penalty term proportional to the dimension of the models. Birgé & Massart [BM97] and Barron, Birgé & Massart [BBM99] generalize this approach, making the link between mode...
متن کاملIntroduction to Kpz
1. A physical introduction 2 1.1. KPZ/Stochastic Burgers/Scaling exponent 2 1.2. Physical derivation 3 1.3. Scaling 3 1.4. Formal invariance of Brownian motion 4 1.5. Dynamic scaling exponent 6 1.6. Renormalization of the nonlinear term 6 1.7. Cutoff KPZ models 7 1.8. Hopf-Cole solutions 8 1.9. Directed polymers in a random environment 11 1.10. Fluctuation breakthroughs of 1999 12 1.11. The Air...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Statistical Mechanics: Theory and Experiment
سال: 2017
ISSN: 1742-5468
DOI: 10.1088/1742-5468/aa6f3e