TY - JOUR

T1 - Longest distance of a non-uniform dispersion process on the infinite line

AU - Shang, Yilun

PY - 2020/12/1

Y1 - 2020/12/1

N2 - The non-uniform dispersion process on the infinite integer line is a synchronous process where n particles are placed at the origin initially, and any particle not exclusively occupying an integer site will move at the next time step to the right adjacent integer with probability pn and to the left with probability 1− pn independently. We characterize the longest distance from the origin when the dispersion process stops, which is shown to be Θ(n) with high probability for fairly general pn.

AB - The non-uniform dispersion process on the infinite integer line is a synchronous process where n particles are placed at the origin initially, and any particle not exclusively occupying an integer site will move at the next time step to the right adjacent integer with probability pn and to the left with probability 1− pn independently. We characterize the longest distance from the origin when the dispersion process stops, which is shown to be Θ(n) with high probability for fairly general pn.

KW - Combinatorial problems

KW - Dispersion

KW - Distance

KW - Particle

KW - Random process

UR - http://www.scopus.com/inward/record.url?scp=85088794269&partnerID=8YFLogxK

U2 - 10.1016/j.ipl.2020.106008

DO - 10.1016/j.ipl.2020.106008

M3 - Article

VL - 164

JO - Information Processing Letters

JF - Information Processing Letters

SN - 0020-0190

M1 - 106008

ER -