Branching Brownian motion in a periodic environment and existence of pulsating traveling waves*

Article Statistics & Probability

Maximum of branching Brownian motion in a periodic environment

Eyal Lubetzky et al.

Summary: The study examines the maximum of Branching Brownian motion (BBM) with varying branching rates in a periodic medium, revealing convergence in distribution of specific subsequences and identifying the limiting distribution. The results highlight the asymptotic shift between the solution to the corresponding F-KPP equation with Heavyside initial data and the pulsating wave.

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES (2022)

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Article Statistics & Probability

Branching Brownian motion in a periodic environment and uniqueness of pulsating traveling waves

Yan-Xia Ren et al.

ADVANCES IN APPLIED PROBABILITY (2022)

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Article Mathematics, Applied

Invariance Principles and Log-Distance of F-KPP Fronts in a Random Medium

Alexander Drewitz et al.

Summary: In this study, we investigated the front of the solution to the F-KPP equation with randomized non-linearity and analyzed its evolution process. By making appropriate assumptions on the randomness, including spatial mixing behavior and boundedness, we obtained a relationship between the front of the solution and the front of the corresponding linearized equation, which can be interpreted as a partial generalization of previous findings in the homogeneous setting. Additionally, we established functional central limit theorems for the fronts of the solutions to both equations.

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS (2022)

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