LAUSR

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 $$ \left( { - R,R} \right) $$-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 $$ C_{ \pm }^{{{\text{out}}({\text{in}})}} \left( {R/W_{sat} } \right)^{{\lambda_{\text{out(in)}} }} $$C±out(in)R/Wsatλout(in). For the generalized outside time scale, we obtain $$ \lambda_{\text{out}} = 1 $$λout=1 whereas $$ \lambda_{\text{in}} < 1 $$λin<1 for the inside case. The parameters $$ C_{ \pm }^{\text{out(in)}} $$C±out(in) are found to be $$ C_{ + }^{\text{out(in)}} \approx C_{ - }^{\text{out(in)}} $$C+out(in)≈C-out(in) in the up–down symmetric models and the model with weak asymmetry whereas $$ C_{ + }^{\text{out(in)}} \ne C_{ - }^{\text{out(in)}} $$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.