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Brunet-Derrida particle systems, free bo...

Durrett, Rick...

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Brunet-Derrida particle systems, free boundary problems and Wiener-Hopf equations by Durrett, Rick ( Author )

Content Provider	Lemonjar Open Access
Publisher	N.A
Publication Date	29-07-2009
Summary	We consider a branching-selection system in R with N particles which give birth independently at rate 1 and where after each birth the leftmost particle is erased, keeping the number of particles constant. We show that, as N→∞, the empirical measure process associated to the system converges in distribution to a deterministic measure-valued process whose densities solve a free boundary integro-differential equation. We also show that this equation has a unique traveling wave solution traveling at speed c or no such solution depending on whether c≥a or c<a, where a is the asymptotic speed of the branching random walk obtained by ignoring the removal of the leftmost particles in our process. The traveling wave solutions correspond to solutions of Wiener-Hopf equations.
ISBN	-
Item Type	Article
File Type	pdf
File Size	36.88 KB
Language	English
Subjects	-
Unlimited	MYR 0.00
Total read	-
URL	https://arxiv.org/abs/0907.5180

Citation

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AMA 11th EditionReferences

Durrett, Rick. Brunet-Derrida particle systems, free boundary problems and Wiener-Hopf equations. N.A. July 29, 2009. Accessed October 01, 2025. https://online.provdatabase.com/cite/12669

APA 7th EditionReferences

Durrett, Rick. (2009). Brunet-Derrida particle systems, free boundary problems and Wiener-Hopf equations. N.A. https://online.provdatabase.com/cite/12669

Chicago 17th EditionReferences

Durrett, Rick. Brunet-Derrida particle systems, free boundary problems and Wiener-Hopf equations. N.A. 2009. https://online.provdatabase.com/cite/12669

HarvardReferences

Durrett, Rick. (2009). Brunet-Derrida particle systems, free boundary problems and Wiener-Hopf equations. [Online]. N.A. Available from: https://online.provdatabase.com/cite/12669. (Accessed 01 October 2025).

Harvard AustraliaReferences

Durrett, Rick, 2009, Brunet-Derrida particle systems, free boundary problems and Wiener-Hopf equations, N.A, viewed 01 October 2025, <https://online.provdatabase.com/cite/12669>

MLA 9th EditionWorks Cited

Durrett, Rick. Brunet-Derrida particle systems, free boundary problems and Wiener-Hopf equations. N.A, 2009. PROV Database, https://online.provdatabase.com/cite/12669.

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