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
SN - 0020-0190
VL - 164
JO - Information Processing Letters
JF - Information Processing Letters
M1 - 106008
ER -