Generalized Survival Probabilities in Height Fluctuations of Limited Mobility Growth Models With and Without Up–Down Symmetry

• Published in: Journal of statistical physics Vol. 176; no. 4; pp. 932 - 945
• Main Authors: Chanphana, R., Chatraphorn, P.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.08.2019; Springer; Springer Nature B.V
• Subjects: Asymmetry; Exponential functions; Growth models; Mathematical and Computational Physics; Physical Chemistry; Physics; Physics and Astronomy; Quantum Physics; Statistical Physics and Dynamical Systems; Survival; Symmetry; Theoretical; Variation; Up–down symmetry; Survival probability; Discrete growth models
• ISSN: 0022-4715; 1572-9613
• DOI: 10.1007/s10955-019-02326-z

The temporal steady-state ordinary and generalized survival probabilities of height fluctuation in limited mobility growth models are studied. The positive and negative survival probabilities, both ordinary and generalized versions, are approximately equal in up–down symmetric models while different in models without the symmetry. The generalized survival probabilities are investigated in both outside and inside - R , R range of height fluctuations. The positive and negative generalized survival time scales, obtained from the exponential decay of the generalized survival probabilities, are observed to vary continuously with R as an exponential function of C ± out ( in ) R / W sat λ out(in) . For the generalized outside time scale, we obtain λ out = 1 whereas λ in < 1 for the inside case. The parameters C ± out(in) are found to be C + out(in) ≈ C - out(in) in the up–down symmetric models and the model with weak asymmetry whereas C + out(in) ≠ C - out(in) in the model with strong asymmetry. The scaling relations of the positive and negative survival probabilities are also presented.