PreprintarXiv licencearXiv
A priori bounds for the generalized parabolic Anderson model in the full subcritical regime
Abstract
We show a priori bounds for the generalized Parabolic Anderson Model (∂t − Δ)u = σ(u) diamond ξ in finite volume in the full subcritical regime. The approach is based on the observation that, for constant initial data, the time interval over which the solution remains close to its initial condition can be chosen uniformly in the value of the initial condition. A comparison principle is then used to extend this estimate to general bounded initial data.
Related
- Stochastic PDE construction of some non-local or non-translation-invariant Anderson operators in the full subcritical regime
- Boundedness of radial solutions to the parabolic-parabolic Keller--Segel system on the plane with subcritical mass
- Parabolic stochastic quantisation of the fractional Φ43 model in the full subcritical regime
- Full asymptotics for the parabolic Anderson model with Pareto potential in the heaviest-tailed regime
- The Green’s function of the parabolic Anderson model and the continuum directed polymer
BibTeX
@misc{esquivel2026priori,
title = {{A priori bounds for the generalized parabolic Anderson model in the full subcritical regime}},
author = {Salvador Esquivel and Felix Schwarzfischer},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.22911},
eprint = {2608.22911},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.22911},
}
RIS
TY - UNPB
TI - A priori bounds for the generalized parabolic Anderson model in the full subcritical regime
AU - Salvador Esquivel
AU - Felix Schwarzfischer
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.22911
UR - https://arxiv.org/abs/2608.22911
AB - We show a priori bounds for the generalized Parabolic Anderson Model (∂_t − Δ)u = σ(u) diamond ξ in finite volume in the full subcritical regime. The approach is based on the observation that, for constant initial data, the time interval over which the solution remains close to its initial condition can be chosen uniformly in the value of the initial condition. A comparison principle is then used to extend this estimate to general bounded initial data.
ER -