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Fluctuation theory for systems of signed and unsigned particles with interaction mechanisms based on intersection local times

Published online by Cambridge University Press:  01 July 2016

Robert J. Adler
Robert J. Adler*
Affiliation:
Technion—Israel Institute of Technology
*
∗Postal address: Faculty of Industrial Engineering and Management, Technion—Israel Institute of Technology, Technion City, Haifa 32000, Israel.
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Abstract

We consider two distinct models of particle systems. In the first we have an infinite collection of identical Markov processes starting at random throughout Euclidean space. In the second a random sign is associated with each process. An interaction mechanism is introduced in each case via intersection local times, and the fluctuation theory of the systems studied as the processes become dense in space. In the first case the fluctuation theory always turns out to be Gaussian, regardless of the order of the intersections taken to introduce the interaction mechanism. In the second case, an interaction mechanism based on kth order intersections leads to a fluctuation theory akin to a :φ k: Euclidean quantum field theory. We consider the consequences of these results and relate them to different models previously studied in the literature.

Keywords

MARKOV PROCESSESINTERACTING PARTICLESGAUSSIAN CHAOSEUCLIDEAN QUANTUM FIELD THEORIES
Type
Research Article
Information
Advances in Applied Probability , Volume 21 , Issue 2 , June 1989 , pp. 334 - 356
Copyright
Copyright © Applied Probability Trust 1989 

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Footnotes

Research supported in part by U.S. Air Force Office of Scientific Research, AFOSR 87–0298.

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