Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 20 min ago
Peer-reviewedCC BYStochastic Partial Differential Equations Analysis and Computations

The Green’s function of the parabolic Anderson model and the continuum directed polymer

  • Tom Alberts
  • Christopher Janjigian
  • Firas Rassoul‐Agha
  • Timo Seppäläinen
Open at sourcePDFDOICite

Abstract

We study the behavior of the coupling of solutions to the stochastic heat equation/parabolic Anderson model (PAM) obtained through convolution with the Green’s function. In this coupling, we show that the PAM with a (sub-)exponentially growing initial condition has conserved quantities given by the slopes at ∞ ∞ and −∞ - ∞ . These are then connected to Hopf–Cole solutions to the KPZ equation and the existence, regularity, and continuity of the quenched continuum polymer measures. We also show that the Green’s function is strictly totally positive using a novel coupling argument based on the continuum directed polymer.

Related

  1. A priori bounds for the generalized parabolic Anderson model in the full subcritical regime
    Salvador Esquivel, Felix Schwarzfischer
    arXivPreprintarXiv licenceFull textAnalysis & PDEsProbabilityarXiv
  2. Full asymptotics for the parabolic Anderson model with Pareto potential in the heaviest-tailed regime
    Nadia Sidorova
    arXivPreprintarXiv licenceFull textProbabilityarXiv
  3. Intermittency for the parabolic Anderson model on spaces with sub-Gaussian heat kernel estimates
    Fabrice Baudoin, Hongyi Chen, Li Chen +1
    arXivPreprintCC BY 4.0Full textProbabilityarXiv
  4. Limit theorems for the one-dimensional parabolic Anderson model with white noise potential
    Kunwoo Kim, Uijun Kim, Jaeyun Yi
    arXivPreprintarXiv licenceFull textProbabilityarXiv
  5. Well--posedness for the continuum Calogero--Moser equations by parabolic regularization
    Yingmo Zhang
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@article{alberts2026greens,
  title = {{The Green’s function of the parabolic Anderson model and the continuum directed polymer}},
  author = {Tom Alberts and Christopher Janjigian and Firas Rassoul‐Agha and Timo Seppäläinen},
  journal = {Stochastic Partial Differential Equations Analysis and Computations},
  year = {2026},
  month = aug,
  doi = {10.1007/s40072-026-00440-0},
  url = {https://doi.org/10.1007/s40072-026-00440-0},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - The Green’s function of the parabolic Anderson model and the continuum directed polymer
AU  - Tom Alberts
AU  - Christopher Janjigian
AU  - Firas Rassoul‐Agha
AU  - Timo Seppäläinen
PY  - 2026
DA  - 2026/08/20
JO  - Stochastic Partial Differential Equations Analysis and Computations
DO  - 10.1007/s40072-026-00440-0
UR  - https://doi.org/10.1007/s40072-026-00440-0
AB  - We study the behavior of the coupling of solutions to the stochastic heat equation/parabolic Anderson model (PAM) obtained through convolution with the Green’s function. In this coupling, we show that the PAM with a (sub-)exponentially growing initial condition has conserved quantities given by the slopes at ∞ ∞ and −∞ - ∞ . These are then connected to Hopf–Cole solutions to the KPZ equation and the existence, regularity, and continuity of the quenched continuum polymer measures. We also show that the Green’s function is strictly totally positive using a novel coupling argument based on the continuum directed polymer.
SN  - 2194-0401
SN  - 2194-041X
ER  -