Mapping spatial persistent large deviations of nonequilibrium surface growth processes onto the temporal persistent large deviations of stochastic random walk processes

摘要

Spatial persistent large deviations probability of surface growth processesgoverned by the Edwards-Wilkinson dynamics, $P_x(x,s)$, with $-1 \leq s \leq 1$is mapped isomorphically onto the temporal persistent large deviationsprobability $P_t(t,s)$ associated with the stochastic Markovian random walkproblem. We show using numerical simulations that the infinite family ofspatial persistent large deviations exponents $\theta_x(s)$ characterizing thepower law decay of $P_x(x,s)$ agrees, as predicted on theoretical grounds byMajumdar and Bray [Phys. Rev. Lett. {\bf 86}, 3700 (2001)] with the numericalmeasurements of $\theta_t(s)$, the continuous family of exponentscharacterizing the long time power law behavior of $P_t(t,s)$. We also discussthe simulations of the spatial persistence probability corresponding to adiscrete model in the Mullins-Herring universality class, where our discretesimulations do not agree well with the theoretical predictions perhaps becauseof the severe finite-size corrections which are known to strongly inhibit themanifestation of the asymptotic continuum behavior in discrete models involvinglarge values of the dynamical exponent and the associated extremely slowconvergence to the asymptotic regime.