Generating constrained run-and-tumble trajectories

Benjamin De Bruyne; Satya N. Majumdar; Gregory Schehr

doi:10.1088/1751-8121/ac1d8e

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arXiv · 2106.03385

Generating constrained run-and-tumble trajectories

Benjamin De Bruyne·Satya N. Majumdar·Gregory Schehr

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Abstract

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.

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BibTeX RIS

Benjamin De Bruyne, Satya N. Majumdar, Gregory Schehr. 2021-06-07. Generating constrained run-and-tumble trajectories. https://doi.org/10.1088/1751-8121%2Fac1d8e

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