Long time scaling behaviour for diffusion with resetting and memory. Boyer, D., Evans, M. R., & Majumdar, S. N. Journal of Statistical Mechanics: Theory and Experiment, 2017(2):023208, 2017. ![Long time scaling behaviour for diffusion with resetting and memory [link]](https://bibbase.org/img/filetypes/link.svg "link")
Paper abstract bibtex 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 ( ##IMG## [http://ej.iop.org/images/1742-5468/2017/2/023208/jstataa58b6ieqn001.gif] ${{\sigma}^{2}}∼t$ ) all the way to anomalous ultraslow growth ##IMG## [http://ej.iop.org/images/1742-5468/2017/2/023208/jstataa58b6ieqn002.gif] ${{\sigma}^{2}}∼\ln \ln t$ .
@article{doi:10.1088/1742-5468/aa58b6,
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 ( ##IMG## [http://ej.iop.org/images/1742-5468/2017/2/023208/jstataa58b6ieqn001.gif] {${{\sigma}^{2}}\sim t$} ) all the way to anomalous ultraslow growth ##IMG## [http://ej.iop.org/images/1742-5468/2017/2/023208/jstataa58b6ieqn002.gif] {${{\sigma}^{2}}\sim \ln \ln t$} .},
Author = {D. Boyer and M. R. Evans and S. N. Majumdar},
Date-Added = {2017-05-08 16:28:18 +0000},
Date-Modified = {2017-05-08 11:29:01 -0500},
Journal = {Journal of Statistical Mechanics: Theory and Experiment},
Number = {2},
Pages = {023208},
Title = {Long time scaling behaviour for diffusion with resetting and memory},
Url = {http://stacks.iop.org/1742-5468/2017/i=2/a=023208},
Volume = {2017},
Year = {2017},
Bdsk-Url-1 = {http://stacks.iop.org/1742-5468/2017/i=2/a=023208}}
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