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The span of one-dimensional multiparticle Brownian motion G. Madhavi Sastry and Noam Agmon
 

Summary: The span of one-dimensional 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 closed-form expression is obtained for the time evolution of the territory covered by N
independently diffusing particles starting from the origin in one-dimension, with and without bias.
For the latter case, the transcendental-approximation derived is essentially exact for any number of
particles. 1996 American Institute of Physics. S0021-9606 96 50208-0
INTRODUCTION
The number of distinct sites visited by a random walker
is considered one of the basic properties in lattice random
walks.1
In one-dimension, 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

  

Source: Agmon, Noam - Institute of Chemistry, Hebrew University of Jerusalem

 

Collections: Chemistry