Fig. 1: Persistence for quenched fBM (type I problem) in d = 1.
From: Everlasting impact of initial perturbations on first-passage times of non-Markovian random walks
a Example of survival probabilities for interface dynamics with H = 3/8 at different temperatures. The slopes of the continuous lines is the value of θ predicted in our approach. b Systematic comparison of θ as measured in simulations versus theoretical values for different T and H = 3/8. c Value of zθ(u) as measured in simulations (squares) by analyzing the statistics of trajectories after the FPT, compared with theoretical values for different θ. Notice the divergences for small u towards ± ∞, which enable us to select the value of θ to minimize these divergences. d Same as b for different H, with T = 0 fixed. "Star'' symbols are the simulation results of ref. 28 (the error bars indicate the confidence intervals given in table 1 of this reference).
