The pushy random walk creates subdiffusively growing obstacle-free cavities in 1D and drives a diffusion-to-localization transition in 2D with subdiffusive cavity radius growth.
Redner, A Guide to First-Passage Processes (Cam- bridge University Press, Cambridge, 2001)
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Stochastic resetting in bounded search processes that feed queues creates a threshold rate beyond which it expands rather than shrinks steady-state convergence regions, with the threshold growing exponentially in the number of servers.
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Diffusion/Subdiffusion in the Pushy Random Walk
The pushy random walk creates subdiffusively growing obstacle-free cavities in 1D and drives a diffusion-to-localization transition in 2D with subdiffusive cavity radius growth.
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Resetting-induced instability in queues fed by a search process in an interval
Stochastic resetting in bounded search processes that feed queues creates a threshold rate beyond which it expands rather than shrinks steady-state convergence regions, with the threshold growing exponentially in the number of servers.