Temporal correlation in the inverse-gamma polymer
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866908480409960448 |
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| author | Basu, Riddhipratim Seppäläinen, Timo Shen, Xiao |
| author_facet | Basu, Riddhipratim Seppäläinen, Timo Shen, Xiao |
| contents | Understanding the decay of correlations in time for (1+1)-dimensional polymer models in the KPZ universality class has been a challenging topic. Following numerical studies by physicists, concrete conjectures were formulated by Ferrari and Spohn (Ferrari-Spohn '16) in the context of planar exponential last passage percolation. These have mostly been resolved by various authors. In the context of positive temperature lattice models, however, these questions have remained open. We consider the time correlation problem for the exactly solvable inverse-gamma polymer in $\mathbb{Z}^2$. We establish, up to constant factors, upper and lower bounds on the correlation between free energy functions for two polymers rooted at the origin (droplet initial condition) when the endpoints are either close together or far apart. We find the same exponents as predicted in (Ferrari-Spohn '16). Our arguments rely on the understanding of stationary polymers, coupling, and random walk comparison. We use recently established moderate deviation estimates for the free energy. In particular, we do not require asymptotic analysis of complicated exact formulae. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_11086 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Temporal correlation in the inverse-gamma polymer Basu, Riddhipratim Seppäläinen, Timo Shen, Xiao Probability 60K35, 60K37 Understanding the decay of correlations in time for (1+1)-dimensional polymer models in the KPZ universality class has been a challenging topic. Following numerical studies by physicists, concrete conjectures were formulated by Ferrari and Spohn (Ferrari-Spohn '16) in the context of planar exponential last passage percolation. These have mostly been resolved by various authors. In the context of positive temperature lattice models, however, these questions have remained open. We consider the time correlation problem for the exactly solvable inverse-gamma polymer in $\mathbb{Z}^2$. We establish, up to constant factors, upper and lower bounds on the correlation between free energy functions for two polymers rooted at the origin (droplet initial condition) when the endpoints are either close together or far apart. We find the same exponents as predicted in (Ferrari-Spohn '16). Our arguments rely on the understanding of stationary polymers, coupling, and random walk comparison. We use recently established moderate deviation estimates for the free energy. In particular, we do not require asymptotic analysis of complicated exact formulae. |
| title | Temporal correlation in the inverse-gamma polymer |
| topic | Probability 60K35, 60K37 |
| url | https://arxiv.org/abs/2305.11086 |