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Abstract
We consider diffusion in arbitrary spatial dimension d with the addition of a resetting process wherein the diffusive particle stochastically resets to a fixed position at a constant rate r. We compute the nonequilibrium stationary state which exhibits nonGaussian behaviour. We then consider the presence of an absorbing target centred at the origin and compute the survival probability and mean time to absorption of the diffusive particle by the target. The mean absorption time is finite and has a minimum value at an optimal resetting rate r which depends on dimension. Finally we consider the problem of a finite density of diffusive particles, each resetting to its own initial position. While the typical survival probability of the target at the origin decays exponentially with time regardless of spatial dimension, the average survival probability decays asymptotically as exp(A(lnt)(d)) where A is a constant. We explain these findings using an interpretation as a renewal process and arguments invoking extreme value statistics.
Original language  English 

Article number  285001 
Number of pages  19 
Journal  Journal of Physics A: Mathematical and Theoretical 
Volume  47 
Issue number  28 
DOIs  
Publication status  Published  18 Jul 2014 
Keywords
 diffusion
 resetting
 firstpassage times
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Dive into the research topics of 'Diffusion with resetting in arbitrary spatial dimension'. Together they form a unique fingerprint.Projects
 1 Finished

Design Principles for New Soft Materials
Cates, M., Allen, R., Clegg, P., Evans, M., MacPhee, C., Marenduzzo, D. & Poon, W.
7/12/11 → 6/06/17
Project: Research
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Martin Evans
 School of Physics and Astronomy  Personal Chair in Statistical Physics
Person: Academic: Research Active