Recently observation of random walks in complex environments like the cell and other glassy systems revealed that the spreading of particles, at its tails, follows a spatial exponential decay instead of the canonical Gaussian. We use the widely applicable continuous time random walk model and obtain the large deviation description of the propagator. Under mild conditions that the microscopic jump lengths distribution is decaying exponentially or faster i.e. Lévy like power law distributed jump lengths are excluded, and that the distribution of the waiting times is analytical for short waiting times, the spreading of particles follows an exponential decay at large distances, with a logarithmic correction. Here we show how anti-bunching of jump events reduces the effect, while bunching and intermittency enhances it. We employ exact solutions of the continuous time random walk model to test the large deviation theory.
Mapping spatial persistent large deviations of nonequilibrium surface growth processes onto the temporal persistent large deviations of stochastic random walk processes
空间持续大偏差概率的表面生长过程所支配的爱德华-威尔金森动力学，$P_x(x,s)$，与$-1 \leq s \leq 1$同构映射到时间持续大偏差概率$P_t(t,s)$与随机马尔可夫随机游动问题。我们使用数值模拟表明，表征$P_x(x,s)$的幂律衰减的空间持续大偏差指数$θ_x(s)$的无限族一致，如Majumdar和Bray [Phys. Rev. Lett. { \bf 86}，3700（2001）]，其中$θ_t(s)$是表征$P_t(t,s)$的长时间幂律行为的指数的连续族。我们还讨论了Mullins-Herring普适类中离散模型的空间持续概率的模拟，我们的离散模拟与理论预测不一致，这可能是因为严重的有限-已知的尺寸修正强烈抑制离散模型中渐近连续行为的表现，该离散模型涉及大的动力学指数值和相关的极慢的收敛到渐近状态。
Large deviations at level 2.5 and for trajectories observables of diffusion processes : the missing parts with respect to their random-walks counterparts
