Number of paths in oriented percolation as zero temperature limit of directed polymer

Ryoki Fukushima, Stefan Junk

Research output: Contribution to journalArticlepeer-review

Abstract

We prove that the free energy of directed polymer in Bernoulli environment converges to the growth rate for the number of open paths in super-critical oriented percolation as the temperature tends to zero. Our proof is based on rate of convergence results which hold uniformly in the temperature. We also prove that the convergence rate is locally uniform in the percolation parameter inside the super-critical phase, which implies that the growth rate depends continuously on the percolation parameter.

Original languageEnglish
Pages (from-to)1119-1151
Number of pages33
JournalProbability Theory and Related Fields
Volume183
Issue number3-4
DOIs
Publication statusPublished - 2022 Aug

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