Daniel ben-Avraham and Éric Brunet 2005 J. Phys. A: Math. Gen. 38 3247 doi:10.1088/0305-4470/38/15/001
Daniel ben-Avraham1 and Éric Brunet2
Show affiliationsThe close similarity between the hierarchies of multiple-point correlation functions for the diffusion-limited coalescence and annihilation processes has caused some recent confusion, raising doubts as to whether such hierarchies uniquely determine an infinite particle system. We elucidate the precise relations between the two processes, arriving at the conclusion that the hierarchy of correlation functions does provide a complete representation of a particle system on the line. We also introduce a new hierarchy of probability density functions for finding particles at specified locations and none in between. This hierarchy is computable for coalescence, through the method of empty intervals, and is naturally suited for questions concerning the ordering of particles on the line.
02.50.-r Probability theory, stochastic processes, and statistics
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
Issue 15 (15 April 2005)
Received 29 December 2004, in final form 22 February 2005
Published 30 March 2005
Daniel ben-Avraham and Éric Brunet 2005 J. Phys. A: Math. Gen. 38 3247
D ben-Avraham et al 2003 J. Phys. A: Math. Gen. 36 1789
V Sood et al 2005 J. Phys. A: Math. Gen. 38 109
Erik M Bollt and Daniel ben-Avraham 2005 New J. Phys. 7 26
Kirill V Larin et al 2003 Phys. Med. Biol. 48 1371
Surabi Menon et al 2010 Environ. Res. Lett. 5 014005
E J Sambriski et al 2009 J. Phys.: Condens. Matter 21 034105
S Webb and D McQuaid 2009 Phys. Med. Biol. 54 4345
Thomas Bortfeld and Steve Webb 2009 Phys. Med. Biol. 54 L35
Thomas Bortfeld and Steve Webb 2009 Phys. Med. Biol. 54 L43