# Survival probability of a run-and-tumble particle in the presence of a drift

@article{DeBruyne2021SurvivalPO, title={Survival probability of a run-and-tumble particle in the presence of a drift}, author={Benjamin De Bruyne and Satya N. Majumdar and Gr{\'e}gory Schehr}, journal={Journal of Statistical Mechanics: Theory and Experiment}, year={2021}, volume={2021} }

We consider a one-dimensional run-and-tumble particle, or persistent random walk, in the presence of an absorbing boundary located at the origin. After each tumbling event, which occurs at a constant rate γ, the (new) velocity of the particle is drawn randomly from a distribution W(v). We study the survival probability S(x, t) of a particle starting from x ⩾ 0 up to time t and obtain an explicit expression for its double Laplace transform (with respect to both x and t) for an arbitrary velocity…

## 9 Citations

### First-order condensation transition in the position distribution of a run-and-tumble particle in one dimension

- MathematicsJournal of Statistical Mechanics: Theory and Experiment
- 2021

We consider a single run-and-tumble particle (RTP) moving in one dimension. We assume that the velocity of the particle is drawn independently at each tumbling from a zero-mean Gaussian distribution…

### Extremal statistics of a one dimensional run and tumble particle with an absorbing wall

- Mathematics
- 2022

. We study the extreme value statistics of a run and tumble particle (RTP) in one dimension till its ﬁrst passage to the origin starting from the position x 0 ( > 0). This model has recently drawn a…

### Generalized run-and-tumble model in 1D geometry for an arbitrary distribution of drift velocities

- Physics
- 2021

In this work, we investigate extensions of the run-and-tumble particle model in 1D. In its simplest version, particle drift is limited to two velocities v = ±v 0 and the model is exactly solvable.…

### From a microscopic solution to a continuum description of interacting active particles

- Physics
- 2022

We consider a model system of persistent random walkers that can jam, pass through each other or jump apart (recoil) on contact. In a continuum limit, where particle motion between stochastic changes…

### A note on the conditional probabilities of the telegraph process

- MathematicsStatistics & Probability Letters
- 2022

### Active random walks in one and two dimensions.

- Mathematics, PhysicsPhysical review. E
- 2022

We investigate active lattice walks: biased continuous time random walks which perform orientational diffusion between lattice directions in one and two spatial dimensions. We study the occupation…

### Active Brownian motion with speed fluctuations in arbitrary dimensions: exact calculation of moments and dynamical crossovers

- PhysicsJournal of Statistical Mechanics: Theory and Experiment
- 2022

We consider the motion of an active Brownian particle with speed fluctuations in d-dimensions in the presence of both translational and orientational diffusion. We use an Ornstein–Uhlenbeck process…

### Run-and-tumble motion in a harmonic potential: field theory and entropy production

- PhysicsJournal of Statistical Mechanics: Theory and Experiment
- 2021

Run-and-tumble (RnT) motion is an example of active motility where particles move at constant speed and change direction at random times. In this work we study RnT motion with diffusion in a harmonic…

### Tuning attraction and repulsion between active particles through persistence

- Mathematics
- 2022

We consider the interplay between persistent motion, which is a generic property of active particles, and a recoil interaction which causes particles to jump apart on contact. The recoil interaction…

## References

SHOWING 1-10 OF 66 REFERENCES

### Universal Survival Probability for a d-Dimensional Run-and-Tumble Particle.

- MathematicsPhysical review letters
- 2020

It is shown that S(t) is independent of d for any finite time t (and not just for large t), as a consequence of the celebrated Sparre Andersen theorem for discrete-time random walks in one dimension.

### Universal properties of a run-and-tumble particle in arbitrary dimension.

- PhysicsPhysical review. E
- 2020

This work considers an active run-and-tumble particle in d dimensions, starting from the origin and evolving over a time interval [0,t], using the Sparre Andersen theorem for discrete-time random walks to compute exactly the probability that the x component does not change sign up to time t, showing that it does not depend on d.

### Noncrossing run-and-tumble particles on a line.

- Mathematics, PhysicsPhysical review. E
- 2019

We study active particles performing independent run-and-tumble motion on an infinite line with velocities v_{0}σ(t), where σ(t)=±1 is a dichotomous telegraphic noise with constant flipping rate γ.…

### Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension

- Mathematics
- 2017

We investigate the motion of a run-and-tumble particle (RTP) in one dimension. We find the exact probability distribution of the particle with and without diffusion on the infinite line, as well as…

### Current fluctuations in noninteracting run-and-tumble particles in one dimension.

- Physics, MathematicsPhysical review. E
- 2020

We present a general framework to study the distribution of the flux through the origin up to time t, in a noninteracting one-dimensional system of particles with a step initial condition with a…

### The convex hull of the run-and-tumble particle in a plane

- MathematicsJournal of Statistical Mechanics: Theory and Experiment
- 2020

We study the statistical properties of the convex hull of a planar run-and-tumble particle (RTP), also known as the ‘persistent random walk’, where the particle/walker runs ballistically between…

### Run and tumble particle under resetting: a renewal approach

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2018

This work considers a particle undergoing run and tumble dynamics, in which its velocity stochastically reverses, in one dimension and shows that the the mean time to absorption is always less for velocity randomization than for position-only resetting.

### Generalised ‘Arcsine’ laws for run-and-tumble particle in one dimension

- MathematicsJournal of Statistical Mechanics: Theory and Experiment
- 2019

The ‘Arcsine’ laws of Brownian particles in one dimension describe distributions of three quantities: the time tm to reach maximum position, the time tr spent on the positive side and the time of the…

### Run-and-tumble particles in two dimensions: Marginal position distributions.

- PhysicsPhysical review. E
- 2020

It is shown that the signature of activity at long times can be found in the atypical fluctuations, which is characterized by computing the large deviation functions explicitly.

### Exact stationary state of a run-and-tumble particle with three internal states in a harmonic trap

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2020

We study the motion of a one-dimensional run-and-tumble particle with three discrete internal states in the presence of a harmonic trap of stiffness The three internal states, corresponding to…