An interacting diffusion model and SK spin glass equation

Xinhong Ding

Stochastic Processes and their Applications, 1994, vol. 54, issue 2, 233-255

Abstract: In this paper we consider a system of N interacting diffusion processes described by Itô stochastic differential equations. We first obtain a McKean-Vlasov limit for the empirical measure associated with the system in the limit as N --> [infinity]. We then consider a special model (which has a "temperature" parameter [beta] > 0) and show that the limiting process exhibits a phase transition phenomenon: for low temperatures ([beta] > [beta]c) it has a unique stable invariant measure while for high temperatures ([beta]

Keywords: Interacting; diffusions; McKean-Vlasov; limit; Neural; networks; Spin; glasses (search for similar items in EconPapers)
Date: 1994
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0304-4149(94)00025-5
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:54:y:1994:i:2:p:233-255

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

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
Bibliographic data for series maintained by Catherine Liu ().