Concentration under scaling limits for weakly pinned Gaussian random walks

Erwin Bolthausen, Tadahisa Funaki*, Tatsushi Otobe

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


We study scaling limits for d-dimensional Gaussian random walks perturbed by an attractive force toward a certain subspace of Rd, especially under the critical situation that the rate functional of the corresponding large deviation principle admits two minimizers. We obtain different type of limits, in a positive recurrent regime, depending on the co-dimension of the subspace and the conditions imposed at the final time under the presence or absence of a wall. The motivation comes from the study of polymers or (1 + 1)-dimensional interfaces with δ-pinning.

Original languageEnglish
Pages (from-to)441-480
Number of pages40
JournalProbability Theory and Related Fields
Issue number3-4
Publication statusPublished - 2009 Mar
Externally publishedYes


  • Concentration
  • Large deviation
  • Minimizers
  • Pinning
  • Random walks
  • Scaling limit

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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