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Large deviation function for the eden model and universality within the one-dimensional kardar-parisi-zhang class
1Laboratoire de Physique Statistique, Ecole Normale Superieure, 24 rue Lhomond, 75231 Paris Cedex 05, France.
Summary
The study supports the universality conjecture for growth systems described by the Kardar-Parisi-Zhang equation. Numerical results for the Eden model indicate the ratio of cumulants approaches a universal value, supporting this theory.
Area of Science:
- Statistical Physics
- Complex Systems
- Dynamical Processes
Background:
- The Kardar-Parisi-Zhang (KPZ) equation describes the dynamics of growing surfaces.
- A conjecture suggests universality in the large deviation function of growth velocity for large systems in 1+1 dimensions.
Purpose of the Study:
- To investigate the universality conjecture for growth systems described by the KPZ equation.
- To examine the ratio of cumulants R(t) as a signature of this universality.
Main Methods:
- Summary of existing numerical and analytical results supporting the conjecture.
- Numerical measurements of the ratio R(t) for the Eden model.
Main Results:
- The ratio of cumulants R(t) for the Eden model was numerically measured.
- Results provide support for the conjecture that R(t) tends towards a universal value.
Conclusions:
- The findings support the universality conjecture for growth systems under the KPZ equation.
- The ratio of cumulants R(t) serves as a key indicator for this universality.