| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Free Univ Berlin, Inst Math, Berlin - Germany
Total Affiliations: 1
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| Document type: | Journal article |
| Source: | ANNALS OF PROBABILITY; v. 49, n. 2, p. 908-943, MAR 2021. |
| Web of Science Citations: | 0 |
| Abstract | |
We study the scaling limit of a branching random walk in static random environment in dimension d = 1, 2 and show that it is given by a superBrownian motion in a white noise potential. In dimension 1 we characterize the limit as the unique weak solution to the stochastic PDE partial derivative t mu=(Delta+xi)mu+root 2 nu mu xi for independent space white noise xi and space-time white noise (xi) over tilde. In dimension 2 the study requires paracontrolled theory and the limit process is described via a martingale problem. In both dimensions we prove persistence of this rough version of the super-Brownian motion. (AU) | |
| FAPESP's process: | 15/50122-0 - Dynamic phenomena in complex networks: basics and applications |
| Grantee: | Elbert Einstein Nehrer Macau |
| Support Opportunities: | Research Projects - Thematic Grants |