Long time scaling behaviour for diffusion with resetting and memory. (9th February 2017) - Boyer, Denis; Evans, Martin R; Majumdar, Satya N
Abstract: We consider a continuous-space and continuous-time diffusion process under resetting with memory. A particle resets to a position chosen from its trajectory in the past according to a memory kernel. Depending on the form of the memory kernel, we show analytically how different asymptotic behaviours of the variance of the particle position emerge at long times. These range from standard diffusive ( σ 2 ∼ t ) all the way to anomalous ultraslow growth σ 2 ∼ ln ln ⁡ t .