Affiliation
Department of Mathematics, University of ArizonaIssue Date
2021-09-16
Metadata
Show full item recordPublisher
IOP PublishingCitation
Gu, Y., & Henderson, C. (2021). A PDE hierarchy for directed polymers in random environments. Nonlinearity.Journal
NonlinearityRights
© 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 2021ISSN
0951-7715EISSN
1361-6544Version
Final accepted manuscriptSponsors
NSFae974a485f413a2113503eed53cd6c53
10.1088/1361-6544/ac23b7