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Transition from Gaussian to non-Gaussian...

Luçon, Eric...

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Transition from Gaussian to non-Gaussian fluctuations for mean-field diffusions in spatial interaction by Luçon, Eric ( Author )

Content Provider	Lemonjar Open Access
Publisher	N.A
Publication Date	02-02-2015
Summary	We consider a system of N disordered mean-field interacting diffusions within spatial constraints: each particle θi is attached to one site xi of a periodic lattice and the interaction between particles θi and θj decreases as \|xi−xj\|−α for α∈[0,1). In a previous work, it was shown that the empirical measure of the particles converges in large population to the solution of a nonlinear partial differential equation of McKean-Vlasov type. The purpose of the present paper is to study the fluctuations associated to this convergence. We exhibit in particular a phase transition in the scaling and in the nature of the fluctuations: when α∈[0,12), the fluctuations are Gaussian, governed by a linear SPDE, with scaling N−−√ whereas the fluctuations are deterministic with scaling N1−α in the case α∈(12,1).
ISBN	-
Item Type	Article
File Type	pdf
File Size	36.88 KB
Language	English
Subjects	-
Unlimited	MYR 0.01
Total read	-
URL	https://arxiv.org/abs/1502.00532

Citation

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AMA 11th EditionReferences

Luçon, Eric. Transition from Gaussian to non-Gaussian fluctuations for mean-field diffusions in spatial interaction. N.A. February 02, 2015. Accessed October 01, 2025. https://online.provdatabase.com/cite/18321

APA 7th EditionReferences

Luçon, Eric. (2015). Transition from Gaussian to non-Gaussian fluctuations for mean-field diffusions in spatial interaction. N.A. https://online.provdatabase.com/cite/18321

Chicago 17th EditionReferences

Luçon, Eric. Transition from Gaussian to non-Gaussian fluctuations for mean-field diffusions in spatial interaction. N.A. 2015. https://online.provdatabase.com/cite/18321

HarvardReferences

Luçon, Eric. (2015). Transition from Gaussian to non-Gaussian fluctuations for mean-field diffusions in spatial interaction. [Online]. N.A. Available from: https://online.provdatabase.com/cite/18321. (Accessed 01 October 2025).

Harvard AustraliaReferences

Luçon, Eric, 2015, Transition from Gaussian to non-Gaussian fluctuations for mean-field diffusions in spatial interaction, N.A, viewed 01 October 2025, <https://online.provdatabase.com/cite/18321>

MLA 9th EditionWorks Cited

Luçon, Eric. Transition from Gaussian to non-Gaussian fluctuations for mean-field diffusions in spatial interaction. N.A, 2015. PROV Database, https://online.provdatabase.com/cite/18321.

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