Occupation time of a run-and-tumble particle with resetting

Physical Review. E
Paul C Bressloff

Abstract

We study the positive occupation time of a run-and-tumble particle (RTP) subject to stochastic resetting. Under the resetting protocol, the position of the particle is reset to the origin at a random sequence of times generated by a Poisson process with rate r. The velocity state is reset to ±v with fixed probabilities ρ_{1} and ρ_{-1}=1-ρ_{1}, where v is the speed. We exploit the fact that the moment-generating functions with and without resetting are related by a renewal equation, and the latter generating function can be calculated by solving a corresponding Feynman-Kac equation. This allows us to numerically locate in Laplace space the largest real pole of the moment-generating function with resetting, and thus derive a large deviation principle (LDP) for the occupation time probability density using the Gartner-Ellis theorem. We explore how the LDP depends on the switching rate α of the velocity state, the resetting rate r, and the probability ρ_{1}. First, we show that the corresponding LDP for a Brownian particle with resetting is recovered in the fast switching limit α→∞. We then consider the case of a finite switching rate. In particular, we investigate how a directional bias in the resetting protocol (ρ_{1}≠0.5) skews...Continue Reading

References

Mar 1, 1993·Physical Review Letters·M Dogterom, S Leibler
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Feb 20, 2010·Bulletin of Mathematical Biology·Jay M Newby, Paul C Bressloff
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Sep 14, 2012·The European Physical Journal. E, Soft Matter·K MartensL Bocquet
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Feb 18, 2017·Physical Review. E·Paul C Bressloff
May 20, 2018·Physical Review. E·Thibaut Demaerel, Christian Maes
Feb 20, 2019·Physical Review. E·Francisco J SevillaEnrique Puga Cital
Jun 20, 2019·Physical Review. E·Paul C Bressloff, Hyunjoong Kim
Sep 11, 2019·Physical Review. E·Pierre Le DoussalGrégory Schehr
Oct 24, 2019·Physical Review. E·Urna BasuArnab Pal
Dec 25, 2019·Physical Review. E·Ydan Ben DorAlexandre P Solon
Apr 4, 2020·Physical Review Letters·Deepak GuptaArnab Pal

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Citations

Jul 10, 2021·Chaos·Karol CapałaEwa Gudowska-Nowak
Jul 18, 2021·Physical Review. E·Francesco MoriGrégory Schehr

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