Probabilistic methods for stationary problems of linear transport theory

Michael Aizenman, Herbert Spohn

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


The steady state of a system of independent particles which undergo elastic collisions can be expressed in terms of the absorption probabilities of the associated Markov process. For the slab albedo problem, this representation enables the application of probabilistic methods to obtain explicit upper and lower bounds on the steady-state density. In particular, the bounds prove the 1/L, decrease of the steady-state flux as a function of the slab width L (Fick's law).

Original languageEnglish (US)
Pages (from-to)23-32
Number of pages10
JournalJournal of Statistical Physics
Issue number1
StatePublished - Jul 1979

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


  • Fick's law
  • Transport equation
  • absorption probabilities
  • slab albedo


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