| Autor: |
Černý, Jiří, Drewitz, Alexander, Oswald, Pascal |
| Rok vydání: |
2022 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
We consider one-dimensional branching Brownian motion in spatially random branching environment (BBMRE) and show that for almost every realisation of the environment, the distributions of the maximal particle of the BBMRE re-centred around its median are tight as time evolves. This result is in stark contrast to the fact that the transition fronts in the solution to the randomised Fisher--Kolmogorov--Petrovskii--Piskunov (F-KPP) equation are, in general, not bounded uniformly in time. In particular, this highlights that -- when compared to the settings of homogeneous branching Brownian motion and the F-KPP equation in a homogeneous environment -- the introduction of a random environment leads to a much more intricate behaviour. |
| Databáze: |
arXiv |
| Externí odkaz: |
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