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On the moments of the (2+1)-dimensional directed polymer and stochastic heat equation in the critical window
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Caravenna, Francesco, Sun, Rongfeng and Zygouras, Nikos (2019) On the moments of the (2+1)-dimensional directed polymer and stochastic heat equation in the critical window. Communications in Mathematical Physics, 372 . pp. 385-440. doi:10.1007/s00220-019-03527-z ISSN 0010-3616.
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WRAP-on-moments-dimensional-polymer-stochastic-heat-window-Zygouras-2019.pdf - Accepted Version - Requires a PDF viewer. Download (797Kb) | Preview |
Official URL: https://doi.org/10.1007/s00220-019-03527-z
Abstract
The partition function of the directed polymer model on Z^{2+ 1} undergoes a phase transition in a suitable continuum and weak disorder limit. In this paper, we focus on a window around the critical point. Exploiting local renewal theorems, we compute the limiting third moment of the space-averaged partition function, showing that it is uniformly bounded. This implies that the rescaled partition functions, viewed as a generalized random field on R^ 2, have non-trivial subsequential limits, and each such limit has the same explicit covariance structure. We obtain analogous results for the stochastic heat equation on R^ 2, extending previous work by Bertini and Cancrini.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | ||||||||
| Library of Congress Subject Headings (LCSH): | Polynomials -- Data processing, Heat equation -- Numerical solutions, Probabilities | ||||||||
| Journal or Publication Title: | Communications in Mathematical Physics | ||||||||
| Publisher: | Springer | ||||||||
| ISSN: | 0010-3616 | ||||||||
| Official Date: | December 2019 | ||||||||
| Dates: |
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| Volume: | 372 | ||||||||
| Page Range: | pp. 385-440 | ||||||||
| DOI: | 10.1007/s00220-019-03527-z | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Reuse Statement (publisher, data, author rights): | This is a post-peer-review, pre-copyedit version of an article published in Communications in Mathematical Physics. The final authenticated version is available online at: https://doi.org/10.1007/s00220-019-03527-z | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 9 September 2019 | ||||||||
| Date of first compliant Open Access: | 29 July 2020 | ||||||||
| RIOXX Funder/Project Grant: |
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