• Login
    View Item 
    •   Home
    • UA Faculty Research
    • UA Faculty Publications
    • View Item
    •   Home
    • UA Faculty Research
    • UA Faculty Publications
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Browse

    All of UA Campus RepositoryCommunitiesTitleAuthorsIssue DateSubmit DateSubjectsPublisherJournalThis CollectionTitleAuthorsIssue DateSubmit DateSubjectsPublisherJournal

    My Account

    LoginRegister

    About

    AboutUA Faculty PublicationsUA DissertationsUA Master's ThesesUA Honors ThesesUA PressUA YearbooksUA CatalogsUA Libraries

    Statistics

    Most Popular ItemsStatistics by CountryMost Popular Authors

    A PDE hierarchy for directed polymers in random environments

    • CSV
    • RefMan
    • EndNote
    • BibTex
    • RefWorks
    Thumbnail
    Name:
    nonlinear-1.pdf
    Size:
    559.8Kb
    Format:
    PDF
    Description:
    Final Accepted Manuscript
    Download
    Author
    Gu, Yu
    Henderson, Christopher
    Affiliation
    Department of Mathematics, University of Arizona
    Issue Date
    2021-09-16
    Keywords
    directed polymer
    reaction-diffusion equation
    stochastic heat equation
    
    Metadata
    Show full item record
    Publisher
    IOP Publishing
    Citation
    Gu, Y., & Henderson, C. (2021). A PDE hierarchy for directed polymers in random environments. Nonlinearity.
    Journal
    Nonlinearity
    Rights
    © 2021 IOP Publishing Ltd & London Mathematical Society.
    Collection Information
    This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.
    Abstract
    For a Brownian directed polymer in a Gaussian random environment, with q(t, ·) denoting the quenched endpoint density and Qn(t,x1,?,xn)=E[q(t,x1) q(txn)], we derive a hierarchical PDE system satisfied by Qn}n=1. We present two applications of the system: (i) we compute the generator of µt(dx)=q(t,xdx}t=0 for some special functionals, where µt(dx)t=0 is viewed as a Markov process taking values in the space of probability measures; (ii) in the high temperature regime with d 3, we prove a quantitative central limit theorem for the annealed endpoint distribution of the diffusively rescaled polymer path. We also study a nonlocal diffusion-reaction equation motivated by the generator and establish a super-diffusive O(t 2/3) scaling.
    Note
    12 month embargo; published: 16 September 2021
    ISSN
    0951-7715
    EISSN
    1361-6544
    DOI
    10.1088/1361-6544/ac23b7
    Version
    Final accepted manuscript
    Sponsors
    NSF
    ae974a485f413a2113503eed53cd6c53
    10.1088/1361-6544/ac23b7
    Scopus Count
    Collections
    UA Faculty Publications

    entitlement

     
    The University of Arizona Libraries | 1510 E. University Blvd. | Tucson, AZ 85721-0055
    Tel 520-621-6442 | repository@u.library.arizona.edu
    DSpace software copyright © 2002-2017  DuraSpace
    Quick Guide | Contact Us | Send Feedback
    Open Repository is a service operated by 
    Atmire NV
     

    Export search results

    The export option will allow you to export the current search results of the entered query to a file. Different formats are available for download. To export the items, click on the button corresponding with the preferred download format.

    By default, clicking on the export buttons will result in a download of the allowed maximum amount of items.

    To select a subset of the search results, click "Selective Export" button and make a selection of the items you want to export. The amount of items that can be exported at once is similarly restricted as the full export.

    After making a selection, click one of the export format buttons. The amount of items that will be exported is indicated in the bubble next to export format.