High temperature limits for (1+1)-Dimensional directed polymer with heavy-tailed disorder

Partha Sarathi Dey, Nikos Zygouras

Research output: Contribution to journalArticle

Abstract

The directed polymer model at intermediate disorder regime was introduced by Alberts-Khanin-Quastel [Ann. Probab. 42 (2014) 1212-1256]. It was proved that at inverse temperature βn -γ with γ = 1/4 the partition function, centered appropriately, converges in distribution and the limit is given in terms of the solution of the stochastic heat equation. This result was obtained under the assumption that the disorder variables posses exponential moments, but its universality was also conjectured under the assumption of six moments. We show that this conjecture is valid and we further extend it by exhibiting classes of different universal limiting behaviors in the case of less than six moments. We also explain the behavior of the scaling exponent for the log-partition function under different moment assumptions and values of γ.

Original languageEnglish (US)
Pages (from-to)4006-4048
Number of pages43
JournalAnnals of Probability
Volume44
Issue number6
DOIs
StatePublished - Jan 1 2016

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Keywords

  • Directed polymer
  • Heavy tail
  • Phase transition
  • Scaling limits

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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