NDLI: Infinite-dimensional stochastic differential equations related to random matrices

Content Provider	Springer Nature Link
Author	Osada, Hirofumi
Copyright Year	2011
Abstract	We solve infinite-dimensional stochastic differential equations (ISDEs) describing an infinite number of Brownian particles interacting via two-dimensional Coulomb potentials. The equilibrium states of the associated unlabeled stochastic dynamics are the Ginibre random point field and Dyson’s measures, which appear in random matrix theory. To solve the ISDEs we establish an integration by parts formula for these measures. Because the long-range effect of two-dimensional Coulomb potentials is quite strong, the properties of Brownian particles interacting with two-dimensional Coulomb potentials are remarkably different from those of Brownian particles interacting with Ruelle’s class interaction potentials. As an example, we prove that the interacting Brownian particles associated with the Ginibre random point field satisfy plural ISDEs.
Ending Page	509
Page Count	39
Starting Page	471
File Format	PDF
ISSN	01788051
e-ISSN	14322064
Journal	Probability Theory and Related Fields
Issue Number	3
Volume Number	153
Language	English
Publisher	Springer-Verlag
Publisher Date	2011-03-15
Publisher Place	Berlin/Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Interacting Brownian particles Coulomb potentials Mathematical and Computational Biology Interacting particle systems Diffusion processes Theoretical, Mathematical and Computational Physics Interacting random processes; statistical mechanics type models; percolation theory Probability Theory and Stochastic Processes Quantitative Finance Infinite-dimensional stochastic differential equations Random matrices Dyson’s model Statistics for Business/Economics/Mathematical Finance/Insurance Continuum models (systems of particles, etc.) Operations Research/Decision Theory Ginibre random point field
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Analysis Statistics, Probability and Uncertainty

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