Large Deviation in Continuous Time Random Walks

Abstract

We discuss large deviation properties of continuous-time random walks (CTRW) and present a general expression for the large deviation rate in CTRW in terms of the corresponding rates for the distributions of steps' lengths and waiting times. In the case of Gaussian distribution of steps' lengths the general expression reduces to a sequence of two Legendre transformations applied to the cumulant generating function of waiting times. The discussion of several examples (Bernoulli and Gaussian random walks with exponentially distributed waiting times, Gaussian random walks with one-sided Lévy and Pareto-distributed waiting times) reveals interesting general properties of such large deviations.

12 pages, 3 figures

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• Large Deviations in Switching Diffusion: from Free Cumulants to Dynamical Transitions
• Dynamically emergent correlations in a Brownian gas with diffusing diffusivity
• Exact height distribution in one-dimensional Edwards-Wilkinson interface with diffusing diffusivity
• Universal and non-universal signatures in the scaling functions of critical variables
• Cusp of non-Gaussian density of particles for a diffusing diffusivity model