Large fluctuations in diffusion-controlled absorption

Baruch Meerson, S. Redner

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14 Scopus citations


Suppose that N0 independently diffusing particles, each with diffusivity D, are initially released at x = ℓ > 0 on the semi-infinite interval 0 x < ∞ with an absorber at x = 0. We determine the probability that N particles survive until time t = T. We also employ macroscopic fluctuation theory to find the most likely history of the system, conditional on there being exactly N survivors at time t = T. Depending on the basic parameter , very different histories can contribute to the extreme cases of N = N0 (all particles survive) and N = 0 (no survivors). For large values of , the leading contribution to comes from an effective point-like quasiparticle that contains all the N0 particles and moves ballistically toward the absorber until absorption occurs.

Original languageAmerican English
Article numberP08008
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number8
StatePublished - 1 Aug 2014


  • diffusion
  • large deviations in nonequilibrium systems
  • stochastic particle dynamics (theory)


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