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Quenched invariance principles for the maximal particle in branching random walk in random environment and the parabolic Anderson model

Černý, Jiří and Drewitz, Alexander. (2020) Quenched invariance principles for the maximal particle in branching random walk in random environment and the parabolic Anderson model. The Annals of Probability, 48 (1). pp. 94-146.

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Official URL: https://edoc.unibas.ch/81597/

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Abstract

We consider branching random walk in spatial random branching environment (BRWRE) in dimension one, as well as related differential equations: the Fisher-KPP equation with random branching and its linearized version, the parabolic Anderson model (PAM). When the random environment is bounded, we show that after recentering and scaling, the position of the maximal particle of the BRWRE, the front of the solution of the PAM, as well as the front of the solution of the randomized Fisher-KPP equation fulfill quenched invariance principles. In addition, we prove that at time t the distance between the median of the maximal particle of the BRWRE and the front of the solution of the PAM is in 0(1110. This partially transfers classical results of Bramson (Comm. Pure Appl. Math. 31 (1978) 531-581) to the setting of BRWRE.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Wahrscheinlichkeitstheorie (Cerny)
UniBasel Contributors:Černý, Jiří
Item Type:Article, refereed
Article Subtype:Research Article
ISSN:0091-1798
Note:Publication type according to Uni Basel Research Database: Journal article
Identification Number:
Last Modified:12 Apr 2021 13:02
Deposited On:12 Apr 2021 13:02

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