TY - JOUR

T1 - Number of paths in oriented percolation as zero temperature limit of directed polymer

AU - Fukushima, Ryoki

AU - Junk, Stefan

N1 - Funding Information:
The authors are grateful to the reviewer for very careful reading. RF was supported by ISHIZUE 2019 of Kyoto University Research Development Program and in part by KAKENHI 17H01093 and 18H03672. SJ was supported by a JSPS Postdoctoral Fellowship for Research in Japan, Grant-in-Aid for JSPS Fellows 19F19814.
Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2022/8

Y1 - 2022/8

N2 - 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.

AB - 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.

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U2 - 10.1007/s00440-022-01130-3

DO - 10.1007/s00440-022-01130-3

M3 - Article

AN - SCOPUS:85130161050

SN - 0178-8051

VL - 183

SP - 1119

EP - 1151

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

IS - 3-4

ER -