### Abstract

Original language | English |
---|---|

Pages (from-to) | 362-370 |

Number of pages | 9 |

Journal | Stochastic Processes and their Applications |

Volume | 125 |

Issue number | 1 |

Early online date | 17 Sep 2014 |

DOIs | |

Publication status | Published - Jan 2015 |

### Fingerprint

### Cite this

*Stochastic Processes and their Applications*,

*125*(1), 362-370. https://doi.org/10.1016/j.spa.2014.09.007

**Phase transition for finite-speed detection among moving particles.** / Sidoravicius, Vladas; Stauffer, A.

Research output: Contribution to journal › Article

*Stochastic Processes and their Applications*, vol. 125, no. 1, pp. 362-370. https://doi.org/10.1016/j.spa.2014.09.007

}

TY - JOUR

T1 - Phase transition for finite-speed detection among moving particles

AU - Sidoravicius, Vladas

AU - Stauffer, A

PY - 2015/1

Y1 - 2015/1

N2 - Consider the model where particles are initially distributed on Zd,d≥2, according to a Poisson point process of intensity λ>0, and are moving in continuous time as independent simple symmetric random walks. We study the escape versus detection problem, in which the target, initially placed at the origin of Zd,d≥2, and changing its location on the lattice in time according to some rule, is said to be detected if at some finite time its position coincides with the position of a particle. For any given S>0S>0, we consider the case where the target can move with speed at most SS, according to any continuous function and can adapt its motion based on the location of the particles. We show that, for any S>0, there exists a sufficiently small λ∗>0, so that if the initial density of particles λ<λ∗, then the target can avoid detection forever.

AB - Consider the model where particles are initially distributed on Zd,d≥2, according to a Poisson point process of intensity λ>0, and are moving in continuous time as independent simple symmetric random walks. We study the escape versus detection problem, in which the target, initially placed at the origin of Zd,d≥2, and changing its location on the lattice in time according to some rule, is said to be detected if at some finite time its position coincides with the position of a particle. For any given S>0S>0, we consider the case where the target can move with speed at most SS, according to any continuous function and can adapt its motion based on the location of the particles. We show that, for any S>0, there exists a sufficiently small λ∗>0, so that if the initial density of particles λ<λ∗, then the target can avoid detection forever.

UR - http://dx.doi.org/10.1016/j.spa.2014.09.007

U2 - 10.1016/j.spa.2014.09.007

DO - 10.1016/j.spa.2014.09.007

M3 - Article

VL - 125

SP - 362

EP - 370

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

IS - 1

ER -