 Interacting Brownian motions in infinite dimensions with logarithmic interaction potentials II: Airy random point fieldHirofumi Osada Stochastic Processes and their Applications, 2013, vol. 123, issue 3, 813-838 Abstract: We give a new sufficient condition of the quasi-Gibbs property. This result is a refinement of one given in a previous paper (Osada (in press) [18]), and will be used in a forthcoming paper to prove the quasi-Gibbs property of Airy random point fields (RPFs) and other RPFs appearing under soft-edge scaling. The quasi-Gibbs property of RPFs is one of the key ingredients to solve the associated infinite-dimensional stochastic differential equation (ISDE). Because of the divergence of the free potentials and the interactions of the finite particle approximation under soft-edge scaling, the result of the previous paper excludes the Airy RPFs, although Airy RPFs are the most significant RPFs appearing in random matrix theory. We will use the result of the present paper to solve the ISDE for which the unlabeled equilibrium state is the Airyβ RPF with β=1,2,4. Keywords: Interacting Brownian particles; Random matrices; Coulomb potentials; Infinitely many particle systems; Diffusions; Airy random point field; Quasi-Gibbs property (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:123:y:2013:i:3:p:813-838 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2012.11.002 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.