 
Summary: The span of onedimensional multiparticle Brownian motion
G. Madhavi Sastry and Noam Agmon
Department of Physical Chemistry and the Fritz Haber Research Center, The Hebrew University,
Jerusalem 91904, Israel
Received 12 September 1995; accepted 14 November 1995
A closedform expression is obtained for the time evolution of the territory covered by N
independently diffusing particles starting from the origin in onedimension, with and without bias.
For the latter case, the transcendentalapproximation derived is essentially exact for any number of
particles. © 1996 American Institute of Physics. S00219606 96 502080
INTRODUCTION
The number of distinct sites visited by a random walker
is considered one of the basic properties in lattice random
walks.1
In onedimension, the ``number of sites'' is equiva
lent to the ``span'' of a diffusion process namely, to the fur
thest point from the origin visited by time t. In the continu
ous limit, the average span is closely related to the first
moment in extrema statistics.2,3
In recent years there has been growing interest in gener
alizing the one particle result to N independent particles.410
