Generating constrained run-and-tumble trajectories

We propose a method to exactly generate bridge run-and-tumble trajectories that are constrained to start at the origin with a given velocity and to return to the origin after a fixed time with another given velocity. The method extends the concept of effective Langevin equations, valid for Markovian...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2021-09, Vol.54 (38), p.385004
Main Authors: De Bruyne, Benjamin, Majumdar, Satya N, Schehr, Grégory
Format: Article
Language:English
Subjects:
Brownian motion
fluctuations
Physics
random walks
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Summary:We propose a method to exactly generate bridge run-and-tumble trajectories that are constrained to start at the origin with a given velocity and to return to the origin after a fixed time with another given velocity. The method extends the concept of effective Langevin equations, valid for Markovian stochastic processes such as Brownian motion, to a non-Markovian stochastic process driven by a telegraphic noise, with exponentially decaying correlations. We obtain effective space-time dependent tumbling rates that implicitly accounts for the bridge constraint. We extend the method to other types of constrained run-and-tumble particles such as excursions and meanders. The method is implemented numerically and is shown to be very efficient.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/ac1d8e