### Abstract

A vicious-walker system consists of N random walkers on a line with any two walkers annihilating each other upon meeting. We study a system of N vicious accelerating walkers with the velocity undergoing Gaussian fluctuations, as opposed to the position. We numerically compute the survival probability exponent, α, for this system, which characterizes the probability for any two walkers not to meet. For example, for N=3, α=0.710.01. Based on our numerical data, we conjecture that is an upper bound on α. We also numerically study N vicious Levy flights and find, for instance, for N=3 and a Levy index μ=1 that α=1.310.03. Vicious accelerating walkers relate to no-crossing configurations of semiflexible polymer brushes and may prove relevant for a non-Markovian extension of Dyson's Brownian motion model.

Original language | English (US) |
---|---|

Article number | 50009 |

Journal | EPL |

Volume | 96 |

Issue number | 5 |

DOIs | |

State | Published - Dec 2011 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*EPL*,

*96*(5), [50009]. https://doi.org/10.1209/0295-5075/96/50009

**Vicious accelerating walkers.** / Xu, S. L Y; Schwarz, Jennifer M.

Research output: Contribution to journal › Article

*EPL*, vol. 96, no. 5, 50009. https://doi.org/10.1209/0295-5075/96/50009

}

TY - JOUR

T1 - Vicious accelerating walkers

AU - Xu, S. L Y

AU - Schwarz, Jennifer M

PY - 2011/12

Y1 - 2011/12

N2 - A vicious-walker system consists of N random walkers on a line with any two walkers annihilating each other upon meeting. We study a system of N vicious accelerating walkers with the velocity undergoing Gaussian fluctuations, as opposed to the position. We numerically compute the survival probability exponent, α, for this system, which characterizes the probability for any two walkers not to meet. For example, for N=3, α=0.710.01. Based on our numerical data, we conjecture that is an upper bound on α. We also numerically study N vicious Levy flights and find, for instance, for N=3 and a Levy index μ=1 that α=1.310.03. Vicious accelerating walkers relate to no-crossing configurations of semiflexible polymer brushes and may prove relevant for a non-Markovian extension of Dyson's Brownian motion model.

AB - A vicious-walker system consists of N random walkers on a line with any two walkers annihilating each other upon meeting. We study a system of N vicious accelerating walkers with the velocity undergoing Gaussian fluctuations, as opposed to the position. We numerically compute the survival probability exponent, α, for this system, which characterizes the probability for any two walkers not to meet. For example, for N=3, α=0.710.01. Based on our numerical data, we conjecture that is an upper bound on α. We also numerically study N vicious Levy flights and find, for instance, for N=3 and a Levy index μ=1 that α=1.310.03. Vicious accelerating walkers relate to no-crossing configurations of semiflexible polymer brushes and may prove relevant for a non-Markovian extension of Dyson's Brownian motion model.

UR - http://www.scopus.com/inward/record.url?scp=82355161492&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=82355161492&partnerID=8YFLogxK

U2 - 10.1209/0295-5075/96/50009

DO - 10.1209/0295-5075/96/50009

M3 - Article

AN - SCOPUS:82355161492

VL - 96

JO - Europhysics Letters

JF - Europhysics Letters

SN - 0295-5075

IS - 5

M1 - 50009

ER -