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F-KPP Scaling limit and selection principle for a Brunet-Derrida type particle system

Groisman, Pablo Jose et al · Cornell University · 2019

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Author / responsible party
Groisman, Pablo Jose et al
Publisher
Cornell University
Year
2019
ISSN
2331-8422
ISSN
2331-8422
Language
English

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We study a particle system with the following diffusion-branching-selection mechanism. Particles perform independent one dimensional Brownian motions and on top of that, at a constant rate, a pair of particles is chosen uniformly at random and both particles adopt the position of the rightmost one among them. We show that the cumulative distribution function of the empirical measure converges to a solution of the Fisher-Kolmogorov-Petrovskii-Piskunov (F-KPP) equation and use this fact to prove that the system selects the minimal macroscopic speed as the number of particles goes to infinity. Fil: Groisman, Pablo Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina Fil: Jonckheere, Matthieu Thimothy Samson. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina

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APA 7

Groisman, P. J. E. A. (2019). F-KPP Scaling limit and selection principle for a Brunet-Derrida type particle system. http://hdl.handle.net/11336/117633

MLA

Groisman, Pablo Jose et al. "F-KPP Scaling limit and selection principle for a Brunet-Derrida type particle system." 2019. http://hdl.handle.net/11336/117633.

Chicago

Groisman, Pablo Jose et al. 2019. "F-KPP Scaling limit and selection principle for a Brunet-Derrida type particle system.". http://hdl.handle.net/11336/117633.

Harvard

Groisman, P. J. E. A. 2019, F-KPP Scaling limit and selection principle for a Brunet-Derrida type particle system, Cornell University, available at: http://hdl.handle.net/11336/117633 [Accessed 8 Aug. 2026].

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Title
F-KPP Scaling limit and selection principle for a Brunet-Derrida type particle system
Author / contributors
Groisman, Pablo Jose et al
Publisher
Cornell University
Publication year
2019
ISSN
2331-8422
ISSN
2331-8422
Language
English

Subjects

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BRANCHING-SELECTION; PARTICLE SYSTEMS; VELOCITY; F-KPP EQUATION; https://purl.org/becyt/ford/1.1; https://purl.org/becyt/ford/1
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