The phenomenon of particle bursts, a well-known feature of PSO is investigated. Their origin is concluded to lie in multiplicative stochasticity, previously encountered in the study of first order stochastic difference equations. The work here demonstrates that bursts contribute to fattening of the tail of the particle position distribution and that these tails are well described by power laws. It is argued that recombinant PSO, a competitive PSO variant without multiplicative randomness, is burst-free. Categories and Subject Descriptors I.2.8 [Artificial Intelligence]: Problem Solving, Control Methods and Search General Terms Algorithms Keywords Particle Swarm Optimisation, Theory