The maximum of the two dimensional Gaussian directed polymer in the subcritical regime
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908276996702208 |
|---|---|
| author | Cosco, Clément Nakajima, Shuta Zeitouni, Ofer |
| author_facet | Cosco, Clément Nakajima, Shuta Zeitouni, Ofer |
| contents | We study the maximum $ϕ_N^*$ of the partition function of the two dimensional (subcritical) Gaussian directed polymer over an $\sqrt N \times \sqrt N$ box. We show that $ϕ_N^*/\log N$ converges towards a constant $σ^*$, which we identify to be the same as for the maximum of a branching random walk with a slowly varying variance profile as studied in Fang-Zeitouni, J. Stat. Phys. 2012 and (in the context of the generalized random energy model) in Bovier-Kurkova, Ann. Inst. H. Poincare 2004. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_17236 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The maximum of the two dimensional Gaussian directed polymer in the subcritical regime Cosco, Clément Nakajima, Shuta Zeitouni, Ofer Probability Primary 60K37, secondary 60K35, 82A51, 82D30 We study the maximum $ϕ_N^*$ of the partition function of the two dimensional (subcritical) Gaussian directed polymer over an $\sqrt N \times \sqrt N$ box. We show that $ϕ_N^*/\log N$ converges towards a constant $σ^*$, which we identify to be the same as for the maximum of a branching random walk with a slowly varying variance profile as studied in Fang-Zeitouni, J. Stat. Phys. 2012 and (in the context of the generalized random energy model) in Bovier-Kurkova, Ann. Inst. H. Poincare 2004. |
| title | The maximum of the two dimensional Gaussian directed polymer in the subcritical regime |
| topic | Probability Primary 60K37, secondary 60K35, 82A51, 82D30 |
| url | https://arxiv.org/abs/2503.17236 |