Comparison of partition functions in a space–time random environment

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1 Citation (Scopus)


Let Z1 and Z2 be partition functions in the random polymer model in the same environment but driven by different underlying random walks. We give a comparison in concave stochastic order between Z1 and Z2 if one of the random walks has “more randomness” than the other. We also treat some related models: The parabolic Anderson model with space–time Lévy noise; Brownian motion among space–time obstacles; and branching random walks in space–time random environments. We also obtain a necessary and sufficient criterion for Z1cvZ2 if the lattice is replaced by a regular tree.

Original languageEnglish
Pages (from-to)95-115
Number of pages21
JournalJournal of Statistical Physics
Issue number1
Publication statusPublished - 2020 Oct 1
Externally publishedYes


  • Directed polymers
  • Random environment
  • Stochastic order

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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